Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs

arXiv:2305.18702v2 Announce Type: replace-cross
Abstract: Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for high-dimensional problems. One fundamental numerical difficulty is that random samples in the training set introduce statistical errors into the discretization of loss functional which may become the dominant error in the final approximation, and therefore overshadow the modeling capability of the neural network. …

abstract adversarial approximation arxiv attention computing cs.lg cs.na differential math.na network neural network numerical pinn random samples sampling stat.ml transport type