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Apr 16

New Adaptive Numerical Methods Based on Dual Formulation of Hyperbolic Conservation Laws

In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative formulations of the same system, are evolved simultaneously. Since nonconservative schemes are known to produce nonphysical weak solutions near discontinuities, we exploit the difference between these two solutions to construct a smoothness indicator (SI). In smooth regions, the difference between the conservative and nonconservative solutions is of the same order as the truncation error of the underlying discretization, whereas in nonsmooth regions, it is {cal O}(1). We apply this idea to the Euler equations of gas dynamics and define the SI using differences in the momentum and pressure variables. This choice allows us to further distinguish neighborhoods of contact discontinuities from other nonsmooth parts of the computed solution. The resulting classification is used to adaptively select numerical discretizations. In the vicinities of contact discontinuities, we employ the low-dissipation central-upwind numerical flux and a second-order piecewise linear reconstruction with the slopes computed using an overcompressive SBM limiter. Elsewhere, we use an alternative weighted essentially non-oscillatory (A-WENO) framework with the central-upwind finite-volume numerical fluxes and either unlimited (in smooth regions) or Ai-WENO-Z (in the nonsmooth regions away from contact discontinuities) fifth-order interpolation. Numerical results for the one- and two-dimensional compressible Euler equations show that the proposed adaptive method improves both the computational efficiency and resolution of complex flow features compared with the non-adaptive fifth-order A-WENO scheme.

  • 4 authors
·
Jan 27

TASAR: Transfer-based Attack on Skeletal Action Recognition

Skeletal sequence data, as a widely employed representation of human actions, are crucial in Human Activity Recognition (HAR). Recently, adversarial attacks have been proposed in this area, which exposes potential security concerns, and more importantly provides a good tool for model robustness test. Within this research, transfer-based attack is an important tool as it mimics the real-world scenario where an attacker has no knowledge of the target model, but is under-explored in Skeleton-based HAR (S-HAR). Consequently, existing S-HAR attacks exhibit weak adversarial transferability and the reason remains largely unknown. In this paper, we investigate this phenomenon via the characterization of the loss function. We find that one prominent indicator of poor transferability is the low smoothness of the loss function. Led by this observation, we improve the transferability by properly smoothening the loss when computing the adversarial examples. This leads to the first Transfer-based Attack on Skeletal Action Recognition, TASAR. TASAR explores the smoothened model posterior of pre-trained surrogates, which is achieved by a new post-train Dual Bayesian optimization strategy. Furthermore, unlike existing transfer-based methods which overlook the temporal coherence within sequences, TASAR incorporates motion dynamics into the Bayesian attack, effectively disrupting the spatial-temporal coherence of S-HARs. For exhaustive evaluation, we build the first large-scale robust S-HAR benchmark, comprising 7 S-HAR models, 10 attack methods, 3 S-HAR datasets and 2 defense models. Extensive results demonstrate the superiority of TASAR. Our benchmark enables easy comparisons for future studies, with the code available in the https://github.com/yunfengdiao/Skeleton-Robustness-Benchmark.

  • 8 authors
·
Sep 4, 2024