English(EN) Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks

随机测试函数、$H^{-1}$ 范数等价性以及随机变分物理信息神经网络

作者 PulseAugur 编辑部 · [2 个来源] · 2026-05-05 09:14

研究人员开发了一种使用随机变分物理信息神经网络（SV-PINNs）求解偏微分方程的新方法。该方法利用了泛函的 $H^{-1}$ 范数与其针对随机测试函数的期望值之间的等价性。SV-PINNs 通过最小化该随机范数的经验近似来训练，为传统的数值方法提供了潜在的范式转变。 AI

影响引入了一种新颖的神经网络训练范式，用于科学计算，有可能提高求解复杂微分方程的准确性和效率。

排序理由该集群包含一篇详细介绍求解微分方程新方法的学术论文。

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$随机测试函数、$H^{-1}$ 范数等价性以及随机变分物理信息神经网络$

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arXiv cs.LG TIER_1 English(EN) · Diego Marcondes · 2026-05-06 04:00

随机测试函数、$H^{-1}$ 范数等价性以及随机变分物理信息神经网络

arXiv:2605.03542v1 Announce Type: cross Abstract: The dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable: evaluating the $H^{-1}$ norm of a residual requires a supre…
arXiv cs.LG TIER_1 English(EN) · Diego Marcondes · 2026-05-05 09:14

随机测试函数、$H^{-1}$ 范数等价性以及随机变分物理信息神经网络

The dual norm characterisation of weak solutions of second-order linear elliptic partial differential equations is mathematically natural but computationally intractable: evaluating the $H^{-1}$ norm of a residual requires a supremum over an infinite-dimensional function space. W…