论文标题
PINNS和GALS：适用于椭圆问题的浅物理知情神经网络的先验错误估计
PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
论文作者
论文摘要
物理学知情的神经网络（PINN）最近在解决部分微分方程的情况下越来越受欢迎，因为它们逃脱了维度的诅咒。在本文中，我们将物理学告知神经网络是一种不确定的点匹配搭配方法，然后在椭圆问题的背景下公开了Galerkin最少正方形（GALS）和PINN之间的连接，以开发先验的错误估计。特别是，属于最小成方限量元件和Rademacher复杂性分析领域的技术用于获得误差估计。
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this paper, we present Physics Informed Neural Networks as an underdetermined point matching collocation method then expose the connection between Galerkin Least Square (GALS) and PINNs, to develop an a priori error estimate, in the context of elliptic problems. In particular, techniques that belong to the realm of least square finite elements and Rademacher complexity analysis are used to obtain the error estimate.
