English(EN) Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation

新研究保证了 SGD 训练的物理信息神经网络的收敛性

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-07 04:00

研究人员已经证明，在求解泊松方程时，随机梯度下降（SGD）训练过参数化两层物理信息神经网络（PINNs）的线性收敛性。该分析考虑了随机优化方法引入的动态随机性，为 SGD 训练的 PINNs 提供了收敛保证，扩展了先前的工作。该分析的关键在于确保训练过程中特定 Gram 矩阵的正定性。 AI

影响为物理信息神经网络的训练提供了理论保证，有可能提高其在解决复杂科学问题中的可靠性。

排序理由在 arXiv 上发表的学术论文，详细说明了特定类型神经网络的收敛保证。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv stat.ML TIER_1 English(EN) · Bangti Jin, Longjun Wu · 2026-07-07 04:00

泊松方程的宽两层物理信息神经网络随机梯度法收敛性

arXiv:2508.21571v2 Announce Type: replace-cross Abstract: Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural n…