Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers

arXiv:2306.17486v3 Announce Type: replace
Abstract: We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning, we obtain a learned neural solver that is faster and scales better than a standard multigrid solver. Our approach offers three main contributions over previous neural methods of this kind. First, we construct a multilevel U-Net-like encoder-solver CNN with an implicit layer on the coarsest grid …

abstract arxiv cnns convolutional neural networks cs.ce cs.lg deep learning equation faster iterative networks neural networks solve solver type via