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

arXiv:2508.21571v2 Announce Type: replace 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 network. Therefore, the convergence guarantee of stochastic gradient descent is of fundamental importance. In this work, we establish the linear convergence of stochastic gradient descent / flow in training over-parameterized two layer PINNs with a general class of activation functions for solving one model second-order ellip