Generalization Error in the Deep Ritz Method with Smooth Activation Functions (Communications in Computational Physics, 2024)
Deep Ritz method is a deep learning paradigm to solve partial differentialequations. In this article we study the generalization error of the Deep Ritz method.We focus on the quintessential problem which is the Poisson’s equation. We show thatgeneralization error of the Deep Ritz method converges to zero with rate $\frac{C}{\sqrt{n}},$ and wediscuss about the constant $C.$ Results are obtained for shallow and residual neuralnetworks with smooth activation functions.