Daily Papers

Dynamic graph representation learning requires capturing both structural relationships and temporal evolution, yet existing approaches face a fundamental trade-off: attention-based methods achieve expressiveness at O(T^2) complexity, while recurrent architectures suffer from gradient pathologies and dense state storage. Spiking neural networks offer event-driven efficiency but remain limited by sequential propagation, binary information loss, and local aggregation that misses global context. We propose ChronoSpike, an adaptive spiking graph neural network that integrates learnable LIF neurons with per-channel membrane dynamics, multi-head attentive spatial aggregation on continuous features, and a lightweight Transformer temporal encoder, enabling both fine-grained local modeling and long-range dependency capture with linear memory complexity O(T cdot d). On three large-scale benchmarks, ChronoSpike outperforms twelve state-of-the-art baselines by 2.0% Macro-F1 and 2.4% Micro-F1 while achieving 3-10times faster training than recurrent methods with a constant 105K-parameter budget independent of graph size. We provide theoretical guarantees for membrane potential boundedness, gradient flow stability under contraction factor ρ< 1, and BIBO stability; interpretability analyses reveal heterogeneous temporal receptive fields and a learned primacy effect with 83-88% sparsity.

The mobility of particles in fluid membranes is a fundamental aspect of many biological processes. In a 1975 paper [1], Saffman and Delbr\"uck demonstrated how the presence of external Stokesian solvents is crucial in regularising the apparently singular flow within an infinite flat membrane. In the present paper, we extend this classical work and compute the rotational mobility of a rigid finite-sized particle located inside a spherical membrane embedded in Stokesian solvents. Treating the particle as a spherical cap, we solve for the flow semi-analytically as a function of the Saffman-Delbr\"uck (SD) length (ratio of membrane to solvent viscosity) and the solid angle formed by the particle. We study the dependence of the mobility and flow on inclusion size and SD length, recovering the flat-space mobility as a special case. Our results will be applicable to a range of biological problems including rotational Brownian motion, the dynamics of lipid rafts, and the motion of aquaporin channels in response to water flow. Our method will provide a novel way of measuring a membrane's viscosity from the rotational diffusion of large inclusions, for which the commonly used planar Saffman-Delbr\"uck theory does not apply.

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we study theoretically the consequences of membrane responsiveness and feedback on the steady-state force--flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, c_0, the driving force, f, and the polymer volume fraction, phi. In our model, solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force--flux relations, j(f), which we quantify in terms of the system's differential permeability, P_sys^{Delta}mathrm{dj}/{df}. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force, and largely tunable by attractive versus repulsive solute--membrane interactions. Moreover, controlling the input, c_0 and f, can lead to steady-state bistability of phi and hysteresis in the force--flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

In this paper, we explore osmotic transport by means of molecular dynamics (MD) simulations. We first consider osmosis through a membrane, and investigate the reflection coefficient of an imperfectly semi-permeable membrane, in the dilute and high concentration regimes. We then explore the diffusion-osmotic flow of a solute-solvent fluid adjacent to a solid surface, driven by a chemical potential gradient parallel to the surface. We propose a novel non-equilibrium MD (NEMD) methodology to simulate diffusion-osmosis, by imposing an external force on every particle, which properly mimics the chemical potential gradient on the solute in spite of the periodic boundary conditions. This NEMD method is validated theoretically on the basis of linear-response theory by matching the mobility with their Green-Kubo expressions. Finally, we apply the framework to more realistic systems, namely a water-ethanol mixture in contact with a silica or a graphene surface.

As one of the energy-efficient alternatives of conventional neural networks (CNNs), spiking neural networks (SNNs) have gained more and more interest recently. To train the deep models, some effective batch normalization (BN) techniques are proposed in SNNs. All these BNs are suggested to be used after the convolution layer as usually doing in CNNs. However, the spiking neuron is much more complex with the spatio-temporal dynamics. The regulated data flow after the BN layer will be disturbed again by the membrane potential updating operation before the firing function, i.e., the nonlinear activation. Therefore, we advocate adding another BN layer before the firing function to normalize the membrane potential again, called MPBN. To eliminate the induced time cost of MPBN, we also propose a training-inference-decoupled re-parameterization technique to fold the trained MPBN into the firing threshold. With the re-parameterization technique, the MPBN will not introduce any extra time burden in the inference. Furthermore, the MPBN can also adopt the element-wised form, while these BNs after the convolution layer can only use the channel-wised form. Experimental results show that the proposed MPBN performs well on both popular non-spiking static and neuromorphic datasets. Our code is open-sourced at https://github.com/yfguo91/MPBN{MPBN}.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this, several generative models have been proposed to generate surrogate trajectories at lower cost. Yet, these models typically learn a fixed-lag transition density, causing the training signal to be dominated by frequent but uninformative transitions. We introduce a new class of generative models, MSM Emulators, which instead learn to sample transitions across discrete states defined by an underlying Markov State Model (MSM). We instantiate this class with Markov Space Flow Matching (MarS-FM), whose sampling offers more than two orders of magnitude speedup compared to implicit- or explicit-solvent MD simulations. We benchmark Mars-FM ability to reproduce MD statistics through structural observables such as RMSD, radius of gyration, and secondary structure content. Our evaluation spans protein domains (up to 500 residues) with significant chemical and structural diversity, including unfolding events, and enforces strict sequence dissimilarity between training and test sets to assess generalization. Across all metrics, MarS-FM outperforms existing methods, often by a substantial margin.

Molecular dynamics (MD) is a central computational tool in physics, chemistry, and biology, enabling quantitative prediction of experimental observables as expectations over high-dimensional molecular distributions such as Boltzmann distributions and transition densities. However, conventional MD is fundamentally limited by the high computational cost required to generate independent samples. Generative molecular dynamics (GenMD) has recently emerged as an alternative, learning surrogates of molecular distributions either from data or through interaction with energy models. While these methods enable efficient sampling, their transferability across molecular systems is often limited. In this work, we show that incorporating auxiliary sources of information can improve the data efficiency and generalization of transferable implicit transfer operators (TITO) for molecular dynamics. We find that coarse-grained TITO models are substantially more data-efficient than Boltzmann Emulators, and that incorporating protein language model (pLM) embeddings further improves out-of-distribution generalization. Our approach, PLaTITO, achieves state-of-the-art performance on equilibrium sampling benchmarks for out-of-distribution protein systems, including fast-folding proteins. We further study the impact of additional conditioning signals -- such as structural embeddings, temperature, and large-language-model-derived embeddings -- on model performance.

The dynamics of biomolecules are crucial for our understanding of their functioning in living systems. However, current 3D imaging techniques, such as cryogenic electron microscopy (cryo-EM), require freezing the sample, which limits the observation of their conformational changes in real time. The innovative liquid-phase electron microscopy (liquid-phase EM) technique allows molecules to be placed in the native liquid environment, providing a unique opportunity to observe their dynamics. In this paper, we propose TEMPOR, a Temporal Electron MicroscoPy Object Reconstruction algorithm for liquid-phase EM that leverages an implicit neural representation (INR) and a dynamical variational auto-encoder (DVAE) to recover time series of molecular structures. We demonstrate its advantages in recovering different motion dynamics from two simulated datasets, 7bcq and Cas9. To our knowledge, our work is the first attempt to directly recover 3D structures of a temporally-varying particle from liquid-phase EM movies. It provides a promising new approach for studying molecules' 3D dynamics in structural biology.

High-resolution brain imaging can now capture not just synapse locations but their molecular composition, with the cost of such mapping falling exponentially. Yet such ultrastructural data has so far told us little about local neuronal physiology - specifically, the parameters (e.g., synaptic efficacies, local conductances) that govern neural dynamics. We propose to translate molecularly annotated ultrastructure into physiology, introducing the concept of an ultrastructure-to-dynamics compiler: a learned mapping from molecularly annotated ultrastructure to simulator-ready, uncertainty-aware physiological parameters. The requirement is paired training data, with jointly acquired ultrastructure from imaging, and dynamical responses to perturbations from physiological experiments. With this data we can train models that predict local physiology directly from structure. Such a compiler would support biophysical simulations by turning anatomical maps into models of circuit dynamics, shifting structure-to-function from a descriptive program to a predictive one and opening routes to understanding neural computation and forecasting intervention effects.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of such a long-stride MD approach. We validate FlashMD's accuracy in reproducing equilibrium and time-dependent properties, using both system-specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

We report DynaCLR, a self-supervised method for embedding cell and organelle Dynamics via Contrastive Learning of Representations of time-lapse images. DynaCLR integrates single-cell tracking and time-aware contrastive sampling to learn robust, temporally regularized representations of cell dynamics. DynaCLR embeddings generalize effectively to in-distribution and out-of-distribution datasets, and can be used for several downstream tasks with sparse human annotations. We demonstrate efficient annotations of cell states with a human-in-the-loop using fluorescence and label-free imaging channels. DynaCLR method enables diverse downstream biological analyses: classification of cell division and infection, clustering heterogeneous cell migration patterns, cross-modal distillation of cell states from fluorescence to label-free channel, alignment of asynchronous cellular responses and broken cell tracks, and discovering organelle response due to infection. DynaCLR is a flexible method for comparative analyses of dynamic cellular responses to pharmacological, microbial, and genetic perturbations. We provide PyTorch-based implementations of the model training and inference pipeline (https://github.com/mehta-lab/viscy) and a GUI (https://github.com/czbiohub-sf/napari-iohub) for the visualization and annotation of trajectories of cells in the real space and the embedding space.

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on R^n defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Gamma-convergence for pairs of phase functions (u_varepsilon,v_varepsilon). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics and `decide' what to do, we propose a minimal axisymmetric model of a spherical active drop, and show that simple and linear interface properties can lead to both steady self-propulsion of the droplet as well as chaotic behavior. The model includes two different mobility mechanisms, namely, diffusiophoresis and the Marangoni effect, that convert self-generated gradients of surfactant concentration into the flow at the droplet surface. In turn, surface-driven flow initiates surfactant advection that is the only nonlinear mechanism and, thus, the only source of dynamical complexity in our model. Numerical investigation of the fully-coupled hydrodynamic and advection diffusion problems reveals that strong advection (e.g., large droplet size) may destabilize a steadily self-propelling drop; once destabilized, the droplet spontaneously stops and a symmetric extensile flow emerges. If advection is strengthened even further in comparison with molecular diffusion, the droplet may perform chaotic oscillations. Our results indicate that the thresholds of these instabilities depend heavily on the balance between diffusiophoresis and the Marangoni effect. Using linear stability analysis, we demonstrate that diffusiophoresis promotes the onset of high-order modes of monotonic instability of the motionless drop. We argue that diffusiophoresis has a similar effect on the instabilities of a moving drop.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds (1fs=10^{-15}s). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of 10^{5} - 10^{6}:fs. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of molecular trajectories as a paradigm for learning flexible multi-task surrogate models of MD from data. By conditioning on appropriately chosen frames of the trajectory, we show such generative models can be adapted to diverse tasks such as forward simulation, transition path sampling, and trajectory upsampling. By alternatively conditioning on part of the molecular system and inpainting the rest, we also demonstrate the first steps towards dynamics-conditioned molecular design. We validate the full set of these capabilities on tetrapeptide simulations and show that our model can produce reasonable ensembles of protein monomers. Altogether, our work illustrates how generative modeling can unlock value from MD data towards diverse downstream tasks that are not straightforward to address with existing methods or even MD itself. Code is available at https://github.com/bjing2016/mdgen.

Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous approaches leverage techniques such as flow or Schrödinger bridge matching to implicitly learn joint trajectories through data snapshots. However, many systems, including biomolecular systems and heterogeneous cell populations, undergo dynamic interactions that evolve over their trajectory and cannot be captured through static snapshots. To close this gap, we introduce Entangled Schrödinger Bridge Matching (EntangledSBM), a framework that learns the first- and second-order stochastic dynamics of interacting, multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles. We define the Entangled Schrödinger Bridge (EntangledSB) problem as solving a coupled system of bias forces that entangle particle velocities. We show that our framework accurately simulates heterogeneous cell populations under perturbations and rare transitions in high-dimensional biomolecular systems.

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose \textbf{Multi-Marginal temporal Schr\"odinger Bridge Matching} (MMtSBM) for video generation from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schr\"odinger Bridge Matching (arXiv:archive/2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real world datasets such as transcriptomic trajectory inference in 100 dimensions, and for the first time recovers couplings and dynamics in very high dimensional image settings. Our work establishes multi-marginal Schr\"odinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

Surface bubbles are an abundant source of aerosols, with important implications for climate processes. In this context, we investigate the stability and thinning dynamics of soap films under effective gravity fields. Experiments are performed using a centrifugal thin-film balance capable of generating accelerations from 0.2 up to 100 times standard gravity, combined with thin-film interferometry to obtain time-resolved thickness maps. Across all experimental conditions, the drainage dynamics are shown to be governed by capillary suction and marginal regeneration-a mechanism in which thick regions of the film are continuously replaced by thin film elements (TFEs) formed at the meniscus. We consistently recover a thickness ratio of 0.8 - 0.9 between the TFEs and the adjacent film, in agreement with previous observations under standard gravity. The measured thinning rates also follow the predicted scaling laws. We identified that gravity has three distinct effects: (i) it induces a strong stretching of the initial film, extending well beyond the linear-elastic regime; (ii) it controls the meniscus size, and thereby the amplitude of the capillary suction and the drainage rate; and (iii) it reveals an inertia-to-viscous transition in the motion of TFEs within the film. These results are supported by theoretical modeling and highlight the robustness of marginal regeneration and capillary-driven drainage under extreme gravity conditions.

Reparameterized diffusion models (RDMs) have recently matched autoregressive methods in protein generation, motivating their use for challenging tasks such as designing membrane proteins, which possess interleaved soluble and transmembrane (TM) regions. We introduce the Membrane Diffusion Language Model (MemDLM), a fine-tuned RDM-based protein language model that enables controllable membrane protein sequence design. MemDLM-generated sequences recapitulate the TM residue density and structural features of natural membrane proteins, achieving comparable biological plausibility and outperforming state-of-the-art diffusion baselines in motif scaffolding tasks by producing lower perplexity, higher BLOSUM-62 scores, and improved pLDDT confidence. To enhance controllability, we develop Per-Token Guidance (PET), a novel classifier-guided sampling strategy that selectively solubilizes residues while preserving conserved TM domains, yielding sequences with reduced TM density but intact functional cores. Importantly, MemDLM designs validated in TOXCAT beta-lactamase growth assays demonstrate successful TM insertion, distinguishing high-quality generated sequences from poor ones. Together, our framework establishes the first experimentally-validated diffusion-based model for rational membrane protein generation, integrating de novo design, motif scaffolding, and targeted property optimization.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor - much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and trajectory inference. However, these methods consider cells as independent data points of population distributions. With spatial transcriptomics, we can represent cellular organization, along with dynamic cell-cell interactions that lead to changes in cell state. Still, key computational advances are necessary to enable the data-driven learning of such complex interactive cellular dynamics. While agent-based modeling (ABM) provides a powerful framework, traditional approaches rely on handcrafted rules derived from domain knowledge rather than data-driven approaches. To address this, we introduce Spatio Temporal Agent-Based Graph Evolution Dynamics(STAGED) integrating ABM with deep learning to model intercellular communication, and its effect on the intracellular gene regulatory network. Using graph ODE networks (GDEs) with shared weights per cell type, our approach represents genes as vertices and interactions as directed edges, dynamically learning their strengths through a designed attention mechanism. Trained to match continuous trajectories of simulated as well as inferred trajectories from spatial transcriptomics data, the model captures both intercellular and intracellular interactions, enabling a more adaptive and accurate representation of cellular dynamics.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Artificially synthesized Janus particles have tremendous prospective as in-vivo drug-delivery agents due to the possibility of self-propulsion by external stimuli. Here we report the first ever computational study of translational and rotational motion of self-propelled Janus tracers in a het- erogeneous polymeric environment. The presence of polymers makes the translational mean square displacement (MSD) of the Janus tracer to grow very slowly as compared to that of a free Janus tracer, but surprisingly the mean square angular displacement (MSAD) is significantly increased as observed in a recent experiment. Moreover, with the increasing propulsion velocity, MSAD grows even faster. However, when the repulsive polymers are replaced with polymers with sticky zones, MSD and MSAD both show sharp decline.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Recent advancements in protein structure determination are revolutionizing our understanding of proteins. Still, a significant gap remains in the availability of comprehensive datasets that focus on the dynamics of proteins, which are crucial for understanding protein function, folding, and interactions. To address this critical gap, we introduce mdCATH, a dataset generated through an extensive set of all-atom molecular dynamics simulations of a diverse and representative collection of protein domains. This dataset comprises all-atom systems for 5,398 domains, modeled with a state-of-the-art classical force field, and simulated in five replicates each at five temperatures from 320 K to 413 K. The mdCATH dataset records coordinates and forces every 1 ns, for over 62 ms of accumulated simulation time, effectively capturing the dynamics of the various classes of domains and providing a unique resource for proteome-wide statistical analyses of protein unfolding thermodynamics and kinetics. We outline the dataset structure and showcase its potential through four easily reproducible case studies, highlighting its capabilities in advancing protein science.

The demand for safe, high-energy-density batteries has spotlighted halide solid-state electrolytes, which offer the potential for enhanced ionic mobility, electrochemical stability, and interfacial deformability. Accelerating their discovery requires extensive molecular dynamics, which has been increasingly enabled by universal machine learning interatomic potentials trained on foundational datasets. However, the dynamic softness of halides poses a stringent test of whether general-purpose models can reliably replace first-principles calculations under the highly distorted, elevated-temperature regimes necessary to probe ion transport. Here, we present AQVolt26, a dataset of 322,656 r^2SCAN single-point calculations for lithium halides, generated via high-temperature configurational sampling across sim5K structures. We demonstrate that foundational datasets provide a strong baseline for stable halide chemistries and transfer local forces well, however absolute energy predictions degrade in distorted higher-temperature regimes. Co-training with AQVolt26 resolves this blind spot. Furthermore, incorporating Materials Project relaxation data improves near-equilibrium performance but degrades extreme-strain robustness without enhancing high-temperature force accuracy. These results demonstrate that domain-specific configurational sampling is essential for the reliable dynamic screening of halide electrolytes. Furthermore, our findings suggest that while foundational models provide a robust base, they are most effective for dynamically soft solid-state chemistries when augmented with targeted, high-temperature data. Finally, we show that near-equilibrium relaxation data serves as a task-specific complement rather than a universally beneficial addition.

We extend our previously proposed image reconstruction method, which allows confocal microscopes to capture periodically moving objects at frequencies beyond their frame rates, to three-dimensional and two-dimensional wide-field imaging. This extension is achieved by implementing a synchronization scheme between a confocal laser scanning microscope and a function generator to ensure consistent initial phase alignment across image sequences acquired at different focal depths or fields of view. The method was demonstrated by visualizing the three-dimensional motion of silica particles attached to an aluminum bar oscillating at 100 Hz and the two-dimensional wide-field response of colloidal particles subjected to periodic pulsed excitation. Quantitative single-particle analysis confirmed that the reconstructed images accurately captured the underlying particle dynamics. The extended approach requires no additional specialized hardware and can be readily integrated with conventional confocal microscopes. Thus, it extends the applicability of confocal imaging to the fast dynamics of periodic processes in biological and soft-matter systems.

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle and demonstrate the well-posedness in suitable time-weighted spaces of the resulting nonlinear and nonlocal system. The solution is furthermore shown to be smooth for positive times. Numerical computations are performed to initiate the study of the long-time behavior of the interface.

Hypothesis: Bacterial contamination of surfaces poses a major threat to public health. Designing effective antibacterial or self-cleaning surfaces requires understanding how bacteria-laden droplets interact with solid substrates and how readily they can be removed. We hypothesize that bacterial motility critically influences the early-stage surface interaction (i.e., surface adhesion) of bacteria-laden droplets, which cannot be captured by conventional contact angle goniometry. Experiments: Sessile droplets containing live and dead Escherichia coli (E. coli) were studied to probe their wetting and interfacial behavior. Contact angle goniometry was used to probe dynamic wetting, while a cantilever-deflection-based method was used to quantify adhesion. Internal flow dynamics were visualized using micro-particle image velocimetry (PIV) and analyzed statistically. Complementary sliding experiments on moderately wettable substrates were performed to assess contact line mobility under tilt. Findings: Despite lower surface tension, droplets containing live bacteria exhibited lower surface adhesion forces than their dead counterparts, with adhesion further decreasing at higher bacterial concentrations. Micro-PIV revealed that flagellated live E. coli actively resist evaporation-driven capillary flow via upstream migration, while at higher concentrations, collective dynamics emerge, producing spatially coherent bacterial motion despite temporal variability. These coordinated flows disrupt passive transport and promote depinning of the contact line, thereby reducing adhesion. Sliding experiments confirmed enhanced contact line mobility and frequent stick-slip motion in live droplets, even with lower receding contact angles and higher hysteresis. These findings provide mechanistic insight into droplet retention, informing the design of self-cleaning/antifouling surfaces.

Ultrafast electron microscopy (UEM) has found widespread applications in physics, chemistry, and materials science, enabling real-space imaging of dynamics on ultrafast timescales. Recent advances have pushed the temporal resolution of UEM into the attosecond regime, enabling the attomicroscopy technique to directly visualize electron motion. In this work, we extend the capabilities of this powerful imaging tool to investigate ultrafast electron dynamics in a biological system by imaging and controlling light induced electronic and chemical changes in the conductive network of multicellular cable bacteria. Using electron energy loss spectroscopy (EELS), we first observed a laser induced increase in {\pi}-electron density, accompanied by spectral peak broadening and a blueshift features indicative of enhanced conductivity and structural modification. We also traced the effect of ultrafast laser pumping on bulk plasmon electron oscillations by monitoring changes in the plasmon like resonance peak. Additionally, we visualized laser induced chemical structural changes in cable bacteria in real space. The imaging results revealed carbon enrichment alongside a depletion of nitrogen and oxygen, highlighting the controllability of chemical dynamics. Moreover, time resolved EELS measurements further revealed a picosecond scale decay and recovery of both {\pi}-electron and plasmonic features, attributed to electron phonon coupling. In addition to shedding light on the mechanism of electron motion in cable bacteria, these findings demonstrate ultrafast modulation and switching of conductivity, underscoring their potential as bio-optoelectronic components operating on ultrafast timescales.

Molecular dynamics (MD) simulations are essential tools for unraveling atomistic insights into the structure and dynamics of condensed-phase systems. However, the universal and accurate prediction of macroscopic properties from ab initio calculations remains a significant challenge, often hindered by the trade-off between computational cost and simulation accuracy. Here, we present ByteFF-Pol, a graph neural network (GNN)-parameterized polarizable force field, trained exclusively on high-level quantum mechanics (QM) data. Leveraging physically-motivated force field forms and training strategies, ByteFF-Pol exhibits exceptional performance in predicting thermodynamic and transport properties for a wide range of small-molecule liquids and electrolytes, outperforming state-of-the-art (SOTA) classical and machine learning force fields. The zero-shot prediction capability of ByteFF-Pol bridges the gap between microscopic QM calculations and macroscopic liquid properties, enabling the exploration of previously intractable chemical spaces. This advancement holds transformative potential for applications such as electrolyte design and custom-tailored solvent, representing a pivotal step toward data-driven materials discovery.

Molecular dynamics (MD) simulations play a crucial role in scientific research. Yet their computational cost often limits the timescales and system sizes that can be explored. Most data-driven efforts have been focused on reducing the computational cost of accurate interatomic forces required for solving the equations of motion. Despite their success, however, these machine learning interatomic potentials (MLIPs) are still bound to small time-steps. In this work, we introduce TrajCast, a transferable and data-efficient framework based on autoregressive equivariant message passing networks that directly updates atomic positions and velocities lifting the constraints imposed by traditional numerical integration. We benchmark our framework across various systems, including a small molecule, crystalline material, and bulk liquid, demonstrating excellent agreement with reference MD simulations for structural, dynamical, and energetic properties. Depending on the system, TrajCast allows for forecast intervals up to 30times larger than traditional MD time-steps, generating over 15 ns of trajectory data per day for a solid with more than 4,000 atoms. By enabling efficient large-scale simulations over extended timescales, TrajCast can accelerate materials discovery and explore physical phenomena beyond the reach of traditional simulations and experiments. An open-source implementation of TrajCast is accessible under https://github.com/IBM/trajcast.

Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish quantitative principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells in quantitative, predictive, and mechanistic ways. We discuss the role of mathematical models in the context of cell-fate decision making systems across the tree of life. Complex multi-cellular organisms have been a particular focus, but single celled organisms also have to sense and respond to their environment. We center our discussion around the idea of design principles which we can learn from observations and modeling, and exploit in order to (re)-design or guide cellular behavior.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

Understanding protein dynamics is critical for elucidating their biological functions. The increasing availability of molecular dynamics (MD) data enables the training of deep generative models to efficiently explore the conformational space of proteins. However, existing approaches either fail to explicitly capture the temporal dependencies between conformations or do not support direct generation of time-independent samples. To address these limitations, we introduce ConfRover, an autoregressive model that simultaneously learns protein conformation and dynamics from MD trajectories, supporting both time-dependent and time-independent sampling. At the core of our model is a modular architecture comprising: (i) an encoding layer, adapted from protein folding models, that embeds protein-specific information and conformation at each time frame into a latent space; (ii) a temporal module, a sequence model that captures conformational dynamics across frames; and (iii) an SE(3) diffusion model as the structure decoder, generating conformations in continuous space. Experiments on ATLAS, a large-scale protein MD dataset of diverse structures, demonstrate the effectiveness of our model in learning conformational dynamics and supporting a wide range of downstream tasks. ConfRover is the first model to sample both protein conformations and trajectories within a single framework, offering a novel and flexible approach for learning from protein MD data.

Machine learning models of cellular interaction dynamics hold promise for understanding cell behavior. Natural killer (NK) cell cytotoxicity is a prominent example of such interaction dynamics and is commonly studied using time-resolved multi-channel fluorescence microscopy. Although tumor cell death events can be annotated at single frames, NK cytotoxic outcome emerges over time from cellular interactions and cannot be reliably inferred from frame-wise classification alone. We introduce BLINK, a trajectory-based recurrent state-space model that serves as a cell world model for NK-tumor interactions. BLINK learns latent interaction dynamics from partially observed NK-tumor interaction sequences and predicts apoptosis increments that accumulate into cytotoxic outcomes. Experiments on long-term time-lapse NK-tumor recordings show improved cytotoxic outcome detection and enable forecasting of future outcomes, together with an interpretable latent representation that organizes NK trajectories into coherent behavioral modes and temporally structured interaction phases. BLINK provides a unified framework for quantitative evaluation and structured modeling of NK cytotoxic behavior at the single-cell level.

The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared to long MD simulations. Our open-source implementation is available at https://github.com/lujiarui/Str2Str

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

High-content screening (HCS) assays based on high-throughput microscopy techniques such as Cell Painting have enabled the interrogation of cells' morphological responses to perturbations at an unprecedented scale. The collection of such data promises to facilitate a better understanding of the relationships between different perturbations and their effects on cellular state. Towards achieving this goal, recent advances in cross-modal contrastive learning could, in theory, be leveraged to learn a unified latent space that aligns perturbations with their corresponding morphological effects. However, the application of such methods to HCS data is not straightforward due to substantial differences in the semantics of Cell Painting images compared to natural images, and the difficulty of representing different classes of perturbations (e.g., small molecule vs CRISPR gene knockout) in a single latent space. In response to these challenges, here we introduce CellCLIP, a cross-modal contrastive learning framework for HCS data. CellCLIP leverages pre-trained image encoders coupled with a novel channel encoding scheme to better capture relationships between different microscopy channels in image embeddings, along with natural language encoders for representing perturbations. Our framework outperforms current open-source models, demonstrating the best performance in both cross-modal retrieval and biologically meaningful downstream tasks while also achieving significant reductions in computation time.

Cell migration in vivo is often guided by chemical signals. Such chemotaxis, such as performed by immune cells migrating to a wound site, is complicated by the complex geometry inside living tissues. In this study, we extend our theoretical model of branched-cell migration on a network by introducing chemokine sources to explore the cellular response. The model predicts a speed-accuracy tradeoff, whereby slow cells are significantly more accurate and able to follow efficiently a weak chemoattractant signal. We then compare the model's predictions with experimental observations of neutrophils migrating to the site of laser-inflicted wound in a zebrafish larva fin, and migrating in-vitro inside a regular lattice of pillars. We find that the model captures the details of the sub-cellular response to the chemokine gradient, as well as the large-scale migration response. This comparison suggests that the neutrophils behave as fast cells, compromising their chemotaxis accuracy, which explains the functionality of these immune cells.

Understanding the dynamic nature of protein structures is essential for comprehending their biological functions. While significant progress has been made in predicting static folded structures, modeling protein motions on microsecond to millisecond scales remains challenging. To address these challenges, we introduce a novel deep learning architecture, Protein Transformer with Scattering, Attention, and Positional Embedding (ProtSCAPE), which leverages the geometric scattering transform alongside transformer-based attention mechanisms to capture protein dynamics from molecular dynamics (MD) simulations. ProtSCAPE utilizes the multi-scale nature of the geometric scattering transform to extract features from protein structures conceptualized as graphs and integrates these features with dual attention structures that focus on residues and amino acid signals, generating latent representations of protein trajectories. Furthermore, ProtSCAPE incorporates a regression head to enforce temporally coherent latent representations.

Altering chemical reactivity and material structure in confined optical environments is on the rise, and yet, a conclusive understanding of the microscopic mechanisms remains elusive. This originates mostly from the fact that accurately predicting vibrational and reactive dynamics for soluted ensembles of realistic molecules is no small endeavor, and adding (collective) strong light-matter interaction does not simplify matters. Here, we establish a framework based on a combination of machine learning (ML) models, trained using density-functional theory calculations, and molecular dynamics to accelerate such simulations. We then apply this approach to evaluate strong coupling, changes in reaction rate constant, and their influence on enthalpy and entropy for the deprotection reaction of 1-phenyl-2-trimethylsilylacetylene, which has been studied previously both experimentally and using ab initio simulations. While we find qualitative agreement with critical experimental observations, especially with regard to the changes in kinetics, we also find differences in comparison with previous theoretical predictions. The features for which the ML-accelerated and ab initio simulations agree show the experimentally estimated kinetic behavior. Conflicting features indicate that a contribution of dynamic electronic polarization to the reaction process is more relevant then currently believed. Our work demonstrates the practical use of ML for polaritonic chemistry, discusses limitations of common approximations and paves the way for a more holistic description of polaritonic chemistry.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

We introduce a technique for extracting microstructural geometry from NMR lineshape analysis in porous materials at angstrom-scale resolution with the use of weak magnetic field gradients. Diverging from the generally held view of FID signals undergoing simple exponential decay, we show that a detailed analysis of the line shape can unravel structural geometry on much smaller scales than previously thought. While the original q-space PFG NMR relies on strong magnetic field gradients in order to achieve high spatial resolution, our current approach reaches comparable or higher resolution using much weaker gradients. As a model system, we simulated gas diffusion for xenon confined within carbon nanotubes over a range of temperatures and nanotube diameters in order to unveil manifestations of confinement in the diffusion behavior. We report a multiscale scheme that couples the above MD simulations with the generalized Langevin equation to estimate the transport properties of interest for this problem, such as diffusivity coefficients and NMR lineshapes, using the Green-Kubo correlation function to correctly evaluate time-dependent diffusion. Our results highlight how NMR methodologies can be adapted as effective means towards structural investigation at very small scales when dealing with complicated geometries. This method is expected to find applications in materials science, catalysis, biomedicine and other areas.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines.

We developed a multiscale approach (MultiSCAAL) that integrates the potential of mean force (PMF) obtained from all-atomistic molecular dynamics simulations with a knowledge-based energy function for coarse-grained molecular simulations in better exploring the energy landscape of a small protein under chemical interference such as chemical denaturation. An excessive amount of water molecules in all-atomistic molecular dynamics simulations often negatively impacts the sampling efficiency of some advanced sampling techniques such as the replica exchange method and it makes the investigation of chemical interferences on protein dynamics difficult. Thus, there is a need to develop an effective strategy that focuses on sampling structural changes in protein conformations rather than solvent molecule fluctuations. In this work, we address this issue by devising a multiscale simulation scheme (MultiSCAAL) that bridges the gap between all-atomistic molecular dynamics simulation and coarse-grained molecular simulation. The two key features of this scheme are the Boltzmann inversion and a protein atomistic reconstruction method we previously developed (SCAAL). Using MultiSCAAL, we were able to enhance the sampling efficiency of proteins solvated by explicit water molecules. Our method has been tested on the folding energy landscape of a small protein Trp-cage with explicit solvent under 8M urea using both the all-atomistic replica exchange molecular dynamics (AA-REMD) and MultiSCAAL. We compared computational analyses on ensemble conformations of Trp-cage with its available experimental NOE distances. The analysis demonstrated that conformations explored by MultiSCAAL better agree with the ones probed in the experiments because it can effectively capture the changes in side chain orientations that can flip out of the hydrophobic pocket in the presence of urea and water molecules.

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the different outcomes when we change the parameters, and/or the initial conditions. We can determine the importance of different factors to influence tumor growth. We discover synergistic therapeutic effects of different treatments and drugs. Cancer is generally untreatable using conventional monotherapy. We consider conventional therapies, oncogene-targeted therapies, tumor-suppressors gene-targeted therapies, immunotherapies, anti-angiogenesis therapies, virotherapy, among others. We need therapies with the potential to target both tumor cells and the tumors' microenvironment. Drugs that target oncogenes and tumor-suppressor genes can be effective in the treatment of some cancers. However, most tumors do reoccur. We have found that the success of the new therapeutic agents can be seen when used in combination with other cancer-cell-killing therapies. Our results have allowed us to design a combinational therapy that can lead to the complete eradication of cancer.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and the expanded availability of experimental 3D protein structures have accelerated structure prediction, the dynamic nature of protein structures has received limited attention. This study introduces an innovative 4D diffusion model incorporating molecular dynamics (MD) simulation data to learn dynamic protein structures. Our approach is distinguished by the following components: (1) a unified diffusion model capable of generating dynamic protein structures, including both the backbone and side chains, utilizing atomic grouping and side-chain dihedral angle predictions; (2) a reference network that enhances structural consistency by integrating the latent embeddings of the initial 3D protein structures; and (3) a motion alignment module aimed at improving temporal structural coherence across multiple time steps. To our knowledge, this is the first diffusion-based model aimed at predicting protein trajectories across multiple time steps simultaneously. Validation on benchmark datasets demonstrates that our model exhibits high accuracy in predicting dynamic 3D structures of proteins containing up to 256 amino acids over 32 time steps, effectively capturing both local flexibility in stable states and significant conformational changes.

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential triangle G=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.

Building a virtual cell capable of accurately simulating cellular behaviors in silico has long been a dream in computational biology. We introduce CellFlux, an image-generative model that simulates cellular morphology changes induced by chemical and genetic perturbations using flow matching. Unlike prior methods, CellFlux models distribution-wise transformations from unperturbed to perturbed cell states, effectively distinguishing actual perturbation effects from experimental artifacts such as batch effects -- a major challenge in biological data. Evaluated on chemical (BBBC021), genetic (RxRx1), and combined perturbation (JUMP) datasets, CellFlux generates biologically meaningful cell images that faithfully capture perturbation-specific morphological changes, achieving a 35% improvement in FID scores and a 12% increase in mode-of-action prediction accuracy over existing methods. Additionally, CellFlux enables continuous interpolation between cellular states, providing a potential tool for studying perturbation dynamics. These capabilities mark a significant step toward realizing virtual cell modeling for biomedical research. Project page: https://yuhui-zh15.github.io/CellFlux/.

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

The classical Coulomb gas model has served as one of the most versatile frameworks in statistical physics, connecting a vast range of phenomena across many different areas. Nonequilibrium generalisations of this model have so far been studied much more scarcely. With the abundance of contemporary research into active and driven systems, one would naturally expect that such generalisations of systems with long-ranged Coulomb-like interactions will form a fertile playground for interesting developments. Here, we present two examples of novel macroscopic behaviour that arise from nonequilibrium fluctuations in long-range interacting systems, namely (1) unscreened long-ranged correlations in strong electrolytes driven by an external electric field and the associated fluctuation-induced forces in the confined Casimir geometry, and (2) out-of-equilibrium critical behaviour in self-chemotactic models that incorporate the particle polarity in the chemotactic response of the cells. Both of these systems have nonlocal Coulomb-like interactions among their constituent particles, namely, the electrostatic interactions in the case of the driven electrolyte, and the chemotactic forces mediated by fast-diffusing signals in the case of self-chemotactic systems. The results presented here hint to the rich phenomenology of nonequilibrium effects that can arise from strong fluctuations in Coulomb interacting systems, and a rich variety of potential future directions, which are discussed.

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

Despite the widespread applications of machine learning force field (MLFF) on solids and small molecules, there is a notable gap in applying MLFF to complex liquid electrolytes. In this work, we introduce BAMBOO (ByteDance AI Molecular Simulation Booster), a novel framework for molecular dynamics (MD) simulations, with a demonstration of its capabilities in the context of liquid electrolytes for lithium batteries. We design a physics-inspired graph equivariant transformer architecture as the backbone of BAMBOO to learn from quantum mechanical simulations. Additionally, we pioneer an ensemble knowledge distillation approach and apply it on MLFFs to improve the stability of MD simulations. Finally, we propose the density alignment algorithm to align BAMBOO with experimental measurements. BAMBOO demonstrates state-of-the-art accuracy in predicting key electrolyte properties such as density, viscosity, and ionic conductivity across various solvents and salt combinations. Our current model, trained on more than 15 chemical species, achieves the average density error of 0.01 g/cm^3 on various compositions compared with experimental data. Moreover, our model demonstrates transferability to molecules not included in the quantum mechanical dataset. We envision this work as paving the way to a "universal MLFF" capable of simulating properties of common organic liquids.

In molecular dynamics (MD) simulations, rare events, such as protein folding, are typically studied by means of enhanced sampling techniques, most of which rely on the definition of a collective variable (CV) along which the acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. Leveraging interpolation progress parameters, we introduce a regression-based learning scheme for CV models, which outperforms classifier-based methods when transition state data is limited and noisy

We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the applied difference of potential and the current across the cell. We show that in the case of anomalous diffusion, the model predicts for the electric impedance of the cell a constant phase element behaviour in the low frequency region. In the parametric curve of the reactance versus the resistance, the slope coincides with the order of the fractional time derivative.

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while machine learning methods have advanced static density prediction, modeling its spatiotemporal dynamics remains largely unexplored. In this work, we introduce a generative framework that combines a 3D convolutional autoencoder with a latent diffusion model (LDM) to learn electron density trajectories from ab-initio molecular dynamics (AIMD) simulations. Our method encodes electron densities into a compact latent space and predicts their future states by sampling from the learned conditional distribution, enabling stable long-horizon rollouts without drift or collapse. To preserve statistical fidelity, we incorporate a scaled Jensen-Shannon divergence regularization that aligns generated and reference density distributions. On AIMD trajectories of liquid lithium at 800 K, our model accurately captures both the spatial correlations and the log-normal-like statistical structure of the density. The proposed framework has the potential to accelerate the simulation of quantum dynamics and overcome key challenges faced by current spatiotemporal machine learning methods as surrogates of quantum mechanical simulators.

In 2000, Gillespie rehabilitated the chemical Langevin equation (CLE) by describing two conditions that must be satisfied for it yield a valid approximation of the chemical master equation (CME). In this work, we construct an original path integral description of the CME, and show how applying Gillespie's two conditions to it directly leads to a path integral equivalent to the CLE. We compare this approach to the path integral equivalent of a large system size derivation, and show that they are qualitatively different. In particular, both approaches involve converting many sums into many integrals, and the difference between the two methods is essentially the difference between using the Euler-Maclaurin formula and using Riemann sums. Our results shed light on how path integrals can be used to conceptualize coarse-graining biochemical systems, and are readily generalizable.

Can a micron sized sack of interacting molecules understand, and adapt to a constantly-fluctuating environment? Cellular life provides an existence proof in the affirmative, but the principles that allow for life's existence are far from being proven. One challenge in engineering and understanding biochemical computation is the intrinsic noise due to chemical fluctuations. In this paper, we draw insights from machine learning theory, chemical reaction network theory, and statistical physics to show that the broad and biologically relevant class of detailed balanced chemical reaction networks is capable of representing and conditioning complex distributions. These results illustrate how a biochemical computer can use intrinsic chemical noise to perform complex computations. Furthermore, we use our explicit physical model to derive thermodynamic costs of inference.

Simulating atomic-scale processes, such as protein dynamics and catalytic reactions, is crucial for advancements in biology, chemistry, and materials science. Machine learning force fields (MLFFs) have emerged as powerful tools that achieve near quantum mechanical accuracy, with promising generalization capabilities. However, their practical use is often limited by long inference times compared to classical force fields, especially when running extensive molecular dynamics (MD) simulations required for many biological applications. In this study, we introduce BoostMD, a surrogate model architecture designed to accelerate MD simulations. BoostMD leverages node features computed at previous time steps to predict energies and forces based on positional changes. This approach reduces the complexity of the learning task, allowing BoostMD to be both smaller and significantly faster than conventional MLFFs. During simulations, the computationally intensive reference MLFF is evaluated only every N steps, while the lightweight BoostMD model handles the intermediate steps at a fraction of the computational cost. Our experiments demonstrate that BoostMD achieves an eight-fold speedup compared to the reference model and generalizes to unseen dipeptides. Furthermore, we find that BoostMD accurately samples the ground-truth Boltzmann distribution when running molecular dynamics. By combining efficient feature reuse with a streamlined architecture, BoostMD offers a robust solution for conducting large-scale, long-timescale molecular simulations, making high-accuracy ML-driven modeling more accessible and practical.

Neural network (NN) potentials promise highly accurate molecular dynamics (MD) simulations within the computational complexity of classical MD force fields. However, when applied outside their training domain, NN potential predictions can be inaccurate, increasing the need for Uncertainty Quantification (UQ). Bayesian modeling provides the mathematical framework for UQ, but classical Bayesian methods based on Markov chain Monte Carlo (MCMC) are computationally intractable for NN potentials. By training graph NN potentials for coarse-grained systems of liquid water and alanine dipeptide, we demonstrate here that scalable Bayesian UQ via stochastic gradient MCMC (SG-MCMC) yields reliable uncertainty estimates for MD observables. We show that cold posteriors can reduce the required training data size and that for reliable UQ, multiple Markov chains are needed. Additionally, we find that SG-MCMC and the Deep Ensemble method achieve comparable results, despite shorter training and less hyperparameter tuning of the latter. We show that both methods can capture aleatoric and epistemic uncertainty reliably, but not systematic uncertainty, which needs to be minimized by adequate modeling to obtain accurate credible intervals for MD observables. Our results represent a step towards accurate UQ that is of vital importance for trustworthy NN potential-based MD simulations required for decision-making in practice.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell death. The model accounts for spatial heterogeneity in both tumor cell density and drug concentration while capturing the complex dynamics of drug resistance development. We first establish the well-posedness of the coupled system by proving the existence and uniqueness of a solution under appropriate regularity conditions. The optimal control problem is then formulated to minimize tumor size while accounting for drug toxicity constraints. Using variational methods, we derive the necessary optimality conditions and characterize the optimal control through an adjoint system. Theoretical results can help to design effective chemotherapy schedules that balance treatment efficacy with adverse effects.

We present a set of numerical simulations of the dynamical evolution of compact planetary systems migrating in a protoplanetary disk whose inner edge is sculpted by the interaction with the stellar magnetic field, as described in Yu et al. (2023). We demonstrate that the resulting final distribution of neighbouring planet period ratios contains only a small surviving fraction of resonant systems, in accordance with observations. The resulting planetary architectures are largely in place by the end of the protoplanetary disk phase (within a few Myr), and do not require significant later dynamical evolution. The divergence of planetary pairs during gas disk dispersal also leads to the excitation of eccentricities when pairs cross mean motion resonances in a divergent fashion. The resulting distribution of remnant free eccentricities is consistent with the values inferred from the observation of transit durations and transit timing variations. We furthermore demonstrate that this conclusion is not significantly altered by tides, assuming standard values for tidal dissipation in Earth or Neptune-class planets. These results demonstrate that the observed spacing and residual dynamical excitation of compact planetary systems can be reproduced by migration through a protoplanetary disk, as long as the inner disk boundary is modelled as a gradual rollover, instead of a sharp transition. Such an effect can be achieved when the model accounts for the diffusion of the stellar magnetic field into the disk. The resulting divergence of planetary pairs during the magnetospheric rebound phase breaks the resonant chains, resulting in a better match to observations than disk models with more traditional inner boundaries.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular systems. However, while classical diffusion sampling usually recovers the training distribution, the corresponding energy-based interpretation of the learned score is often inconsistent with this distribution, even for low-dimensional toy systems. We trace this inconsistency to inaccuracies of the learned score at very small diffusion timesteps, where the model must capture the correct evolution of the data distribution. In this regime, diffusion models fail to satisfy the Fokker--Planck equation, which governs the evolution of the score. We interpret this deviation as one source of the observed inconsistencies and propose an energy-based diffusion model with a Fokker--Planck-derived regularization term to enforce consistency. We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins, and by introducing a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and achieves improved consistency and efficient sampling. Our code, model weights, and self-contained JAX and PyTorch notebooks are available at https://github.com/noegroup/ScoreMD.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Many examples of cooperation exist in biology. In chemical systems however, which can sometimes be quite complex, we do not appear to observe intricate cooperative interactions. A key question for the origin of life, is then how can molecular cooperation first arise in an abiotic system prior to the emergence of biological replication. We postulate that selection at the molecular level is a driving force behind the complexification of chemical systems, particularly during the origins of life. In the theory of multilevel selection the two selective forces are: within-group and between-group, where the former tends to favor "selfish" replication of individuals and the latter favor cooperation between individuals enhancing the replication of the group as a whole. These forces can be quantified using the Price equation, which is a standard tool used in evolutionary biology to quantify evolutionary change. Our central claim is that replication and heredity in chemical systems are subject to selection, and quantifiable using the multilevel Price equation. We demonstrate this using the Graded Autocatalysis Replication Domain computer model, describing simple protocell composed out of molecules and its replication, which respectively analogue to the group and the individuals. In contrast to previous treatments of this model, we treat the lipid molecules themselves as replicating individuals and the protocells they form as groups of individuals. Our goal is to demonstrate how evolutionary biology tools and concepts can be applied in chemistry and we suggest that molecular cooperation may arise as a result of group selection. Further, the biological relation of parent-progeny is proposed to be analogue to the reactant-product relation in chemistry, thus allowing for tools from evolutionary biology to be applied to chemistry and would deepen the connection between chemistry and biology.

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the CME, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

Diatoms have been described as nanometer-born lithographers because of their ability to create sophisticated three-dimensional amorphous silica exoskeletons. The hierarchical architecture of these structures provides diatoms with mechanical protection and the ability to filter, float, and manipulate light. Therefore, they emerge as an extraordinary model of multifunctional materials from which to draw inspiration. In this paper, we use numerical simulations, analytical models, and experimental tests to unveil the structural and fluid dynamic efficiency of the Coscinodiscus species diatom. Then we propose a novel 3D printable multifunctional biomimetic material for applications such as porous filters, heat exchangers, drug delivery systems, lightweight structures, and robotics. Our results demonstrate the role of Nature as a material designer for efficient and tunable systems and highlight the potential of diatoms for engineering materials innovation. Additionally, the results reported in this paper lay the foundation to extend the structure-property characterization of diatoms.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Chemical potential of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot satisfy a constant chemical potential condition as solute species can migrate to the interface and deplete the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative constant chemical potential molecular dynamics (iCuMD) simulation, which helps simulate targeted molar concentrations of species in solution. iCuMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target concentration (chemical potential). We demonstrate our approach using solid-liquid and liquid-air interfacial systems as case studies. Specifically, we perform classical force field-based MD simulations of NaCl(aq)-air and NaCl(aq)-graphite interfaces and machine learning interatomic potential (MLIP)-based MD simulations of the Na2SO4(aq)-graphene interface. Our results show that the iCuMD approach efficiently achieves the desired bulk ion concentration within two iterations and can also be integrated with MLIP-driven simulations which enable constant potential simulations with DFT-level accuracy. We show that iCuMD offers a robust and simple computational framework for constant chemical potential simulations as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Self-supervised pretraining from static structures of drug-like compounds and proteins enable powerful learned feature representations. Learned features demonstrate state of the art performance on a range of predictive tasks including molecular properties, structure generation, and protein-ligand interactions. The majority of approaches are limited by their use of static structures and it remains an open question, how best to use atomistic molecular dynamics (MD) simulations to develop more generalized models to improve prediction accuracy for novel molecular structures. We present SURrogate mmGBSA (SurGBSA) as a new modeling approach for MD-based representation learning, which learns a surrogate function of the Molecular Mechanics Generalized Born Surface Area (MMGBSA). We show for the first time the benefits of physics-informed pre-training to train a surrogate MMGBSA model on a collection of over 1.4 million 3D trajectories collected from MD simulations of the CASF-2016 benchmark. SurGBSA demonstrates a dramatic 27,927x speedup versus a traditional physics-based single-point MMGBSA calculation while nearly matching single-point MMGBSA accuracy on the challenging pose ranking problem for identification of the correct top pose (-0.4% difference). Our work advances the development of molecular foundation models by showing model improvements when training on MD simulations. Models, code and training data are made publicly available.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Foundation models applied to bio-molecular space hold promise to accelerate drug discovery. Molecular representation is key to building such models. Previous works have typically focused on a single representation or view of the molecules. Here, we develop a multi-view foundation model approach, that integrates molecular views of graph, image and text. Single-view foundation models are each pre-trained on a dataset of up to 200M molecules and then aggregated into combined representations. Our multi-view model is validated on a diverse set of 18 tasks, encompassing ligand-protein binding, molecular solubility, metabolism and toxicity. We show that the multi-view models perform robustly and are able to balance the strengths and weaknesses of specific views. We then apply this model to screen compounds against a large (>100 targets) set of G Protein-Coupled receptors (GPCRs). From this library of targets, we identify 33 that are related to Alzheimer's disease. On this subset, we employ our model to identify strong binders, which are validated through structure-based modeling and identification of key binding motifs.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

Modeling cellular states and predicting their responses to perturbations are central challenges in computational biology and the development of virtual cells. Existing foundation models for single-cell transcriptomics provide powerful static representations, but they do not explicitly model the distribution of cellular states for generative simulation. Here, we introduce Lingshu-Cell, a masked discrete diffusion model that learns transcriptomic state distributions and supports conditional simulation under perturbation. By operating directly in a discrete token space that is compatible with the sparse, non-sequential nature of single-cell transcriptomic data, Lingshu-Cell captures complex transcriptome-wide expression dependencies across approximately 18,000 genes without relying on prior gene selection, such as filtering by high variability or ranking by expression level. Across diverse tissues and species, Lingshu-Cell accurately reproduces transcriptomic distributions, marker-gene expression patterns and cell-subtype proportions, demonstrating its ability to capture complex cellular heterogeneity. Moreover, by jointly embedding cell type or donor identity with perturbation, Lingshu-Cell can predict whole-transcriptome expression changes for novel combinations of identity and perturbation. It achieves leading performance on the Virtual Cell Challenge H1 genetic perturbation benchmark and in predicting cytokine-induced responses in human PBMCs. Together, these results establish Lingshu-Cell as a flexible cellular world model for in silico simulation of cell states and perturbation responses, laying the foundation for a new paradigm in biological discovery and perturbation screening.

In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propulsion is increased. However, the range of self-propulsions in which a pure liquid regime exist appears to vanish upon approaching the so-called "jamming point" at which solidity of soft-sphere packings is lost. Such an "active yielding" transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existent of different universality classes for the yielding transition under different driving conditions. In addition, we present direct measurements of length and time scales for both driving scenarios. A comparison with theoretical predictions from recent literature reveals poor agreement with our numerical results.

Drug-protein binding and dissociation dynamics are fundamental to understanding molecular interactions in biological systems. While many tools for drug-protein interaction studies have emerged, especially artificial intelligence (AI)-based generative models, predictive tools on binding/dissociation kinetics and dynamics are still limited. We propose a novel research paradigm that combines molecular dynamics (MD) simulations, enhanced sampling, and AI generative models to address this issue. We propose an enhanced sampling strategy to efficiently implement the drug-protein dissociation process in MD simulations and estimate the free energy surface (FES). We constructed a program pipeline of MD simulations based on this sampling strategy, thus generating a dataset including 26,612 drug-protein dissociation trajectories containing about 13 million frames. We named this dissociation dynamics dataset DD-13M and used it to train a deep equivariant generative model UnbindingFlow, which can generate collision-free dissociation trajectories. The DD-13M database and UnbindingFlow model represent a significant advancement in computational structural biology, and we anticipate its broad applicability in machine learning studies of drug-protein interactions. Our ongoing efforts focus on expanding this methodology to encompass a broader spectrum of drug-protein complexes and exploring novel applications in pathway prediction.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput comparable to legacy static implementations while retaining high-level flexibility. We investigate the Laplacian growth instability across varying injection geometries and walker concentrations. Our analysis confirms the robustness of the standard fractal dimension D_f approx 1.71 for dilute regimes, consistent with the Witten-Sander universality class. However, we report a distinct crossover to Eden-like compact growth (D_f approx 1.87) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized Rényi dimensions and lacunarity metrics to quantify the monofractal character and spatial heterogeneity of the aggregates. This work establishes a reproducible, open-source testbed for exploring phase transitions in non-equilibrium statistical mechanics.

The study of the long-time dynamics of quantum systems can be a real challenge, especially in systems like ultracold gases, where the required timescales may be longer than the lifetime of the system itself. In this work, we show that it is possible to access the long-time dynamics of a strongly repulsive atomic gas mixture in shorter times. The shortcut-to-dynamics protocol that we propose does not modify the fate of the observables, but effectively jumps ahead in time without changing the system's inherent evolution. Just like the next-chapter button in a movie player that allows to quickly reach the part of the movie one wants to watch, it is a leap into the future.

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the membrane itself is governed by the convexified F\"{o}ppl's model. The uniqueness of this model lies in the convexity of its variational formulation despite the inherent nonlinearity of the strain-displacement relation. It makes it possible to rewrite the optimization problem as a pair of mutually dual convex variational problems. In the primal problem a linear functional is maximized with respect to displacement functions while enforcing that point-wisely the strain lies in an unbounded closed convex set. The dual problem consists in finding equilibrated stresses that are to minimize a convex integral functional of linear growth defined on the space of Radon measures. The pair of problems is analysed: existence and regularity results are provided, together with the system of optimality criteria. To demonstrate the computational potential of the pair, a finite element scheme is developed around it. Upon reformulation to a conic-quadratic & semi-definite programming problem, the method is employed to produce numerical simulations for several load case scenarios.

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger Bridge Matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct outcomes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

Machine-learned coarse-grained (CG) models often suffer from noisy training data, limiting their accuracy and transferability. We propose a method to generate low-noise training data based on the potential of mean force by constraining CG beads during atomistic simulations and accumulating time-averaged forces. Implemented within the neuroevolution potential (NEP) framework, our approach achieves training accuracy comparable to atomistic models trained on density functional theory data. For liquid water, the NEP-CG model accurately reproduces densities from 1 bar to 1 GPa, successfully extrapolating beyond the 0.5 GPa training limit, with a virial correction essential for the correct equation of state. For an anisotropic C_{60} monolayer, distinguishing crystallographically distinct bead types reduces stress errors by an order of magnitude and captures directional thermal conductivity. We further introduce a multiscale NEP-AACG model integrating all-atom (AA) and CG degrees of freedom, demonstrated for gold nanowire fracture at an experimentally relevant strain rate. Computational speeds for NEP-CG models reach hundreds to thousands of ns/day using a single consumer-grade GPU. This work provides a robust framework for constructing accurate, transferable, and efficient CG models across diverse systems.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Proteins are dynamic molecular machines whose biological functions, spanning enzymatic catalysis, signal transduction, and structural adaptation, are intrinsically linked to their motions. Designing proteins with targeted dynamic properties, however, remains a challenge due to the complex, degenerate relationships between sequence, structure, and molecular motion. Here, we introduce VibeGen, a generative AI framework that enables end-to-end de novo protein design conditioned on normal mode vibrations. VibeGen employs an agentic dual-model architecture, comprising a protein designer that generates sequence candidates based on specified vibrational modes and a protein predictor that evaluates their dynamic accuracy. This approach synergizes diversity, accuracy, and novelty during the design process. Via full-atom molecular simulations as direct validation, we demonstrate that the designed proteins accurately reproduce the prescribed normal mode amplitudes across the backbone while adopting various stable, functionally relevant structures. Notably, generated sequences are de novo, exhibiting no significant similarity to natural proteins, thereby expanding the accessible protein space beyond evolutionary constraints. Our work integrates protein dynamics into generative protein design, and establishes a direct, bidirectional link between sequence and vibrational behavior, unlocking new pathways for engineering biomolecules with tailored dynamical and functional properties. This framework holds broad implications for the rational design of flexible enzymes, dynamic scaffolds, and biomaterials, paving the way toward dynamics-informed AI-driven protein engineering.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the extreme near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the near-contact limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the capsize determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model -- and its qualitative and at times quantitative accuracy -- on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, and chemical reactions. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry.

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

In recent years, groundbreaking advancements in natural language processing have culminated in the emergence of powerful large language models (LLMs), which have showcased remarkable capabilities across a vast array of domains, including the understanding, generation, and translation of natural language, and even tasks that extend beyond language processing. In this report, we delve into the performance of LLMs within the context of scientific discovery, focusing on GPT-4, the state-of-the-art language model. Our investigation spans a diverse range of scientific areas encompassing drug discovery, biology, computational chemistry (density functional theory (DFT) and molecular dynamics (MD)), materials design, and partial differential equations (PDE). Evaluating GPT-4 on scientific tasks is crucial for uncovering its potential across various research domains, validating its domain-specific expertise, accelerating scientific progress, optimizing resource allocation, guiding future model development, and fostering interdisciplinary research. Our exploration methodology primarily consists of expert-driven case assessments, which offer qualitative insights into the model's comprehension of intricate scientific concepts and relationships, and occasionally benchmark testing, which quantitatively evaluates the model's capacity to solve well-defined domain-specific problems. Our preliminary exploration indicates that GPT-4 exhibits promising potential for a variety of scientific applications, demonstrating its aptitude for handling complex problem-solving and knowledge integration tasks. Broadly speaking, we evaluate GPT-4's knowledge base, scientific understanding, scientific numerical calculation abilities, and various scientific prediction capabilities.

Spatial proteomics technologies have transformed our understanding of complex tissue architectures by enabling simultaneous analysis of multiple molecular markers and their spatial organization. The high dimensionality of these data, varying marker combinations across experiments and heterogeneous study designs pose unique challenges for computational analysis. Here, we present Virtual Tissues (VirTues), a foundation model framework for biological tissues that operates across the molecular, cellular and tissue scale. VirTues introduces innovations in transformer architecture design, including a novel tokenization scheme that captures both spatial and marker dimensions, and attention mechanisms that scale to high-dimensional multiplex data while maintaining interpretability. Trained on diverse cancer and non-cancer tissue datasets, VirTues demonstrates strong generalization capabilities without task-specific fine-tuning, enabling cross-study analysis and novel marker integration. As a generalist model, VirTues outperforms existing approaches across clinical diagnostics, biological discovery and patient case retrieval tasks, while providing insights into tissue function and disease mechanisms.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended beta-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Large-scale cell microscopy screens are used in drug discovery and molecular biology research to study the effects of millions of chemical and genetic perturbations on cells. To use these images in downstream analysis, we need models that can map each image into a feature space that represents diverse biological phenotypes consistently, in the sense that perturbations with similar biological effects have similar representations. In this work, we present the largest foundation model for cell microscopy data to date, a new 1.9 billion-parameter ViT-G/8 MAE trained on over 8 billion microscopy image crops. Compared to a previous published ViT-L/8 MAE, our new model achieves a 60% improvement in linear separability of genetic perturbations and obtains the best overall performance on whole-genome biological relationship recall and replicate consistency benchmarks. Beyond scaling, we developed two key methods that improve performance: (1) training on a curated and diverse dataset; and, (2) using biologically motivated linear probing tasks to search across each transformer block for the best candidate representation of whole-genome screens. We find that many self-supervised vision transformers, pretrained on either natural or microscopy images, yield significantly more biologically meaningful representations of microscopy images in their intermediate blocks than in their typically used final blocks. More broadly, our approach and results provide insights toward a general strategy for successfully building foundation models for large-scale biological data.

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how every single cell decides to position itself relative to its neighboring cells. Despite its importance, it remains a major challenge to understand and predict the behavior of every cell within the living tissue over time during such intricate processes. To tackle this question, we propose a geometric deep learning model that can predict multicellular folding and embryogenesis, accurately capturing the highly convoluted spatial interactions among cells. We demonstrate that multicellular data can be represented with both granular and foam-like physical pictures through a unified graph data structure, considering both cellular interactions and cell junction networks. We successfully use our model to achieve two important tasks, interpretable 4-D morphological sequence alignment, and predicting local cell rearrangements before they occur at single-cell resolution. Furthermore, using an activation map and ablation studies, we demonstrate that cell geometries and cell junction networks together regulate local cell rearrangement which is critical for embryo morphogenesis. This approach provides a novel paradigm to study morphogenesis, highlighting a unified data structure and harnessing the power of geometric deep learning to accurately model the mechanisms and behaviors of cells during development. It offers a pathway toward creating a unified dynamic morphological atlas for a variety of developmental processes such as embryogenesis.

We prove stability for a class of heterogeneous catalysis models in the L_p-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms. Cancer networks are special cases of developmental control networks. Cancer results from transformations of normal developmental networks. Our theory generates a natural classification of all possible cancers based on their network architecture. Each cancer network has a unique topology and semantics and developmental dynamics that result in distinct clinical tumor phenotypes. We apply this new theory with a series of proof of concept cases for all the basic cancer types. These cases have been computationally modeled, their behavior simulated and mathematically described using a multicellular systems biology approach. There are fascinating correspondences between the dynamic developmental phenotype of computationally modeled {\em in silico} cancers and natural {\em in vivo} cancers. The theory lays the foundation for a new research paradigm for understanding and investigating cancer. The theory of cancer networks implies that new diagnostic methods and new treatments to cure cancer will become possible.

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation. Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and stochastic forces -- to represent both autonomous and non-autonomous processes in neural systems. Crucially, the potential function is parameterized as a network of locally coupled oscillators, biasing the model toward oscillatory and flow-like behaviors observed in biological neural populations. Our model features a recurrent encoder, a one-layer Transformer decoder, and Langevin dynamics in the latent space. Empirically, our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor, closely matching ground-truth firing rates. On the Neural Latents Benchmark (NLB), the model achieves superior held-out neuron likelihoods (bits per spike) and forward prediction accuracy across four challenging datasets. It also matches or surpasses alternative methods in decoding behavioral metrics such as hand velocity. Overall, this work introduces a flexible, physics-inspired, high-performing framework for modeling complex neural population dynamics and their unobserved influences.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.