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English(EN) Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs

PINNs可能无法学习到正确的Hamilton-Jacobi解

作者 PulseAugur 编辑部 · [1 个来源] ·

一篇新的研究论文探讨了物理信息神经网络（PINNs）在求解Hamilton-Jacobi-Isaacs方程时的局限性。研究发现，通常通过采样偏微分方程残差的大小来判断解的PINNs，可能会收敛到不正确的“粘性解”，这些解满足零测度集上的方程，但本质上是错误的。研究人员确定了确保PINNs学习到正确的粘性解所必需的特定参数化和结构诊断方法，尤其是在复杂几何和更高维度的情况下。 AI

影响 强调了在使用神经网络进行复杂科学建模时可能存在的陷阱，并强调了稳健验证方法的必要性。

排序理由 研究论文，详细介绍了特定机器学习技术在求解数学方程时的局限性。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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PINNs可能无法学习到正确的Hamilton-Jacobi解

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研究论文，详细介绍了特定机器学习技术在求解数学方程时的局限性。[lever_c_demoted from research: ic=1 ai=1.0]
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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Raul Jimenez, Pablo Tejerina-P\'erez, Leonid Sarieddine, Pedro Taranc\'on-\'Alvarez, Marisol Traforetti, Pau Sol\'e-Vilar\'o, Oleksii Ignatenko, Nazar Tkach, Pavlos Protopapas ·

    残差低，数值错：用PINNs学习Hamilton-Jacobi-Isaacs方程的粘性解

    arXiv:2610.27193v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation an…

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