---
license: cc-by-4.0
pretty_name: Linear Radiation Transport (Lattice + Hohlraum)
tags:
  - physics
  - radiation-transport
  - scientific-machine-learning
  - surrogate-modeling
  - nuclear engineering
  - physicsnemo
  - kit-rt
size_categories:
  - 1K<n<10K
---

## Dataset Description:
A surrogate-modeling dataset for the 2-D linear
**Radiation Transport Equation (RTE)**, covering two canonical benchmarks
that vary along complementary axes:

- **Lattice** (707 samples, 494 train / 106 val / 107 test) — fixed
  `7 × 7` block geometry; per-sample variation in the white-background
  scattering coefficient \\(\sigma_s^W\\) and the blue-absorber cross-
  section \\(\sigma_a^B\\) drawn from a discrete design grid (see
  § Data generation). QoI: final-time absorption integral
  \\(\int_B \sigma_a\, \phi\, dx\\) over the absorbing blocks.

  ![Lattice layout](docs/images/lattice_layout.png)

- **Hohlraum** (846 samples, 592 train / 126 val / 128 test) — fixed
  per-region cross-sections; per-sample variation in 8 geometry
  parameters (`ulr, llr, urr, lrr, hlr, hrr, cx, cy`) controlling the
  inner edges and y-extents of two wall-anchored red strips and the
  (x, y) offset of a center insert (see § Data generation). QoI:
  final-time absorption integral \\(\int_S \sigma_a\, \phi\, dx\\)
  evaluated over three material regions
  \\(S \in \{\text{center insert},\ \text{vertical strip},\ \text{horizontal strip}\}\\).

  ![Hohlraum layout](docs/images/hohlraum_layout.png)

The dataset contains initial and final timesteps.

## Data generation

Simulations were produced with [KiT-RT](https://github.com/KiT-RT) using
a discrete-ordinate (S_N) angular discretization, a finite-volume scheme
on an unstructured mesh, and an explicit SSP Runge-Kutta time integrator,
then curated into the PhysicsNeMo `Mesh` memmap format. Both benchmarks
sweep their per-sample parameters over a **discrete design grid** rather
than continuous uniform random sampling.

**Lattice.** The design set is the full Cartesian product of
\\(\sigma_a^B \in \{5, 7.5, \ldots, 102.5\}\\) and
\\(\sigma_s^W \in \{0.1, 0.6, \ldots, 9.6\}\\), with spacings 2.5 and 0.5
respectively, giving **800** unique parameter configurations. Of these,
**707** yielded complete and valid simulations.

**Hohlraum.** The full design set contains \\(3^8 = 6561\\) configurations
formed from three prescribed values for each of the eight geometry
parameters:

| Parameter family | Values |
|---|---|
| Top red-strip edges (`ulr`, `urr`) | \\(\{0.3,\ 0.4,\ 0.5\}\\) |
| Bottom red-strip edges (`llr`, `lrr`) | \\(\{-0.5,\ -0.4,\ -0.3\}\\) |
| Right interior red-strip edge (`hrr`) | \\(\{0.5,\ 0.6,\ 0.63\}\\) |
| Left interior red-strip edge (`hlr`) | \\(\{-0.63,\ -0.6,\ -0.5\}\\) |
| Capsule center (`cx`, `cy`) | \\(\{-0.1,\ 0,\ 0.1\} \times \{-0.075,\ 0,\ 0.075\}\\) |

From this grid, **1000** configurations were sampled uniformly at random
without replacement, yielding **846** complete and valid simulations.
Incomplete runs were mainly due to scheduling, timeouts, or other
infrastructure failures rather than known simulation-code failures.

## How to download

The dataset is **not** a `datasets`-loadable Parquet dataset; it ships
PhysicsNeMo `tensordict` memmap stores packed as **one tarball per
benchmark** (`mesh/lattice.tar.gz`, `mesh/hohlraum.tar.gz`). Download
the full repo and extract both tarballs in place:

```python
import tarfile
from pathlib import Path
from huggingface_hub import snapshot_download

local_dir = Path(snapshot_download(
    repo_id="nvidia/Linear-Radiation-Transport",
    repo_type="dataset",
    local_dir="./rte",        # or omit to use the HF cache
))

for arc in (local_dir / "mesh").glob("*.tar.gz"):
    with tarfile.open(arc) as tf:
        tf.extractall(arc.parent, filter="data")
```

After extraction you'll have `mesh/lattice/<name>.pmsh/` and
`mesh/hohlraum/<name>.pmsh/` directories, each loadable with PhysicsNeMo's
`Mesh` API alongside the matching `<name>.attrs.json` sidecar.

## Example surrogate-modeling results

The figures below are produced by the
[PhysicsNeMo radiation-transport example](https://github.com/NVIDIA/physicsnemo/tree/main/examples/nuclear_engineering/radiation_transport)
on one held-out test sample per benchmark. Each panel shows the
ground-truth final-time scalar flux, the Transolver prediction, and the
absolute error, sharing the same color scale within a row.

![Lattice: target, prediction, absolute error of final-time flux](docs/images/transolver_lattice.png)

![Hohlraum: target, prediction, absolute error of final-time flux](docs/images/transolver_hohlraum.png)

See the example's `README.md` for the training recipe, inference
commands, and the QoI / per-region metrics that accompany these
predictions.

## Dataset Owner(s):
NVIDIA Corporation

## Dataset Creation Date:
May 2026

## License/Terms of Use:
[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/)

## Intended Usage:
Training, evaluation, and benchmarking of point-cloud / mesh-based neural
surrogates for final-time linear radiation transport. The two
benchmarks are complementary stress tests: Lattice probes the surrogate's
ability to generalise across **material parameters** at fixed geometry,
while Hohlraum probes generalisation across **geometry** at fixed
material parameters. Suitable for graph neural networks, neural operators,
point-cloud regressors, and mixed-fidelity / uncertainty-quantification
studies that build on KiT-RT reference solutions.

## Dataset Characterization
** Data Collection Method<br>
* [Synthetic] - High-resolution KiT-RT (S_N + finite-volume) simulations
  on unstructured triangular meshes, post-processed into PhysicsNeMo
  `Mesh` memmap stores. <br>


** Labeling Method<br>
* [Synthetic] - Per-cell scalar flux and derived per-region absorption
  QoIs are computed directly by the numerical solver; no human labeling
  is involved. <br>

## Dataset Format
- **Modality**: 2-D point cloud / unstructured-mesh, per-cell tensors
  plus per-simulation scalar metadata.
- **Per-sample container**: PhysicsNeMo `Mesh` (a tensordict memmap
  store) shipped on disk as a `<name>.pmsh/` directory plus a
  `<name>.attrs.json` sidecar.
- **On-Hub packing**: one `tar.gz` per benchmark
  (`mesh/lattice.tar.gz`, `mesh/hohlraum.tar.gz`). Each archive
  contains a top-level `<bench>/` directory holding all of that
  benchmark's `<name>.pmsh/` + `<name>.attrs.json` files. This keeps
  the file count low for fast, rate-limit-friendly downloads.
- **Per-cell fields**: `cell_areas` (float32), `sigma_a`, `sigma_s`,
  `sigma_t` (float32), `Q` (float32), `material_properties` (int64),
  `scalar_flux` (float32, shape `(N, 2)` for initial + final snapshots).
- **Cell-center coordinates**: `Mesh.points` (float32, `(N, 2)` — the
  simulations are 2-D so points are stored without a z column).
- **Per-simulation fields** (`Mesh.global_data`): `sim_times` / `timesteps`
  / `wall_times`, `flux_statistics`, `global_metrics`, plus flattened
  `attr__*` parameter draws.
- **Splits**: full train/val/test splits at
  `splits/{lattice,hohlraum}_splits.json`.
- **Stats**: per-field flux and material-property normalization stats at
  `stats/{lattice,hohlraum}_{flux,material}_stats.yaml`.
- **Auxiliary**: PNG schematics under `docs/images/`.

## Dataset Quantification
- **Record count**: 1,553 simulations covered by the train/val/test splits
  (707 Lattice + 846 Hohlraum).
- **Cells per sample**: lattice ≈79.9k (constant); hohlraum ≈70k–81k.
- **Per-cell features per sample**: 7 fields (cell_areas, sigma_a,
  sigma_s, sigma_t, Q, material_properties, scalar_flux) plus 2-D
  cell-center coordinates and per-simulation metadata.
- **Total storage**: ~7.2 GB for the extracted `.pmsh/` directories;
  ~1.6 GB as the per-benchmark `mesh/{lattice,hohlraum}.tar.gz`
  archives shipped to the Hugging Face Hub (gzip-compressed).

## Reference(s):
- Schotthöfer, S., & Hauck, C. (2025). "Reference solutions for linear
  radiation transport: the Hohlraum and Lattice benchmarks."
  *arXiv preprint* [arXiv:2505.17284](https://arxiv.org/abs/2505.17284).
- Kusch, J., Schotthöfer, S., Stammer, P., Wolters, J., & Xiao, T.
  (2023). "KiT-RT: An extendable framework for radiative transfer and
  therapy." *ACM Transactions on Mathematical Software*, **49**(4), 1–24.
- KiT-RT solver: <https://github.com/KiT-RT>.

## Ethical Considerations:
NVIDIA believes Trustworthy AI is a shared responsibility and we have established policies and practices to enable development for a wide array of AI applications.  When downloaded or used in accordance with our terms of service, developers should work with their internal developer teams to ensure this dataset meets requirements for the relevant industry and use case and addresses unforeseen product misuse.   
Please report quality, risk, security vulnerabilities or NVIDIA AI Concerns here.