Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations

arXiv:2404.18538v1 Announce Type: new
Abstract: Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of efficient tools for dealing with the interfaces between two adjacent sub-domains heavily hinders the training effects, even leads to the discontinuity of the learned solutions. In this paper, we propose a symmetry group based domain decomposition strategy to enhance the PINN …

abstract arxiv cs.lg differential domain networks neural networks physics physics-informed pinn solve struggle symmetry tools type