Convergence Rate Analysis For Deep Ritz Method With ReLU-ResNet

This paper analyzes the convergence rate of the deep Ritz method(DRM)with ReLU-ResNet,where the error depends on the depth and width of the network and the number of samples explicitly.Hence we can properly choose the structure of networks in terms of the number of training samples.The main idea of proof is to divide the total error of the deep Ritz method into three parts:approximation error,statistical error and optimization error.We derive an upper bound on the approximation error of ReLU-ResNet in₁norm and bound the statistical error via Rademacher complexity.Numerical examples are shown to verify accuracy of the deep Ritz method with ReLU-ResNet for high-dimensional problems.