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math.NA2023
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…
math.NA2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Yuling Jiao, Yanming Lai, Yang Wang +2
This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on with Diric…