English(EN) Learning functional components of PDEs from data using neural networks

神经网络从数据中推断偏微分方程中未知的函数

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-10 04:00

研究人员开发了一种新颖的方法，利用神经网络来推断偏微分方程（PDE）中未知的函数分量。该方法将神经网络直接嵌入PDE框架中，从而能够在训练过程中从数据中学习函数。通过非局部聚合-扩散方程的演示，该方法能够从稳态观测中成功推断出相互作用核和外部势，为增强PDE模型的预测能力提供了一种途径。 AI

影响通过推断PDE中未知的函数项，增强了科学模型的预测能力。

排序理由关于一种新颖的科学建模机器学习方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Torkel E. Loman, Yurij Salmaniw, Antonio Leon Villares, Jose A. Carrillo, Ruth E. Baker · 2026-09-10 04:00

使用神经网络从数据中学习偏微分方程的函数分量

arXiv:2602.13174v2 Announce Type: replace Abstract: Partial differential equation (PDE) models frequently contain unknown functional terms that cannot be measured directly, limiting their predictive utility. While data-driven methods for estimating scalar PDE parameters are well …