论文标题
使用线性PDE的神经网络对残留最小化的错误估计
Error estimates of residual minimization using neural networks for linear PDEs
论文作者
论文摘要
我们提出了一个抽象框架，用于分析最小二乘方法的收敛，基于残留最小化，当可行的解决方案是神经网络时。借助规范关系和紧凑性论证，我们得出了以强和弱形式的残留最小化的连续和离散表述的错误估计。该配方涵盖了最近基于强和变分的配方开发了物理知识的神经网络。
We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physics-informed neural networks based on strong and variational formulations.
