Cv-PINN: Efficient learning of variational physics-informed neural network with domain decomposition

Abstract

We propose a novel approach for tackling scientific problems governed by differential equations, based on the concept of a physics-informed neural networks (PINNs). The method involves evaluating the residuals of equations on subdomains of the computational zone via numerical integration. Test functions and integral weights are embedded within convolutional filters to extract information from these residuals. Our approach demonstrates exceptional parallel abilities when dealing with computational zones featuring large numbers of sub-domains, proving significantly more efficient than variational physics-informed neural networks with domain decomposition (hp-VPINNs). By utilizing domain decomposition, we can further enhance the precision of our predictions when dealing with complex functions. In comparison to PINNs, our approach boasts superior accuracy when fitting intricate functions. Additionally, we showcase the efficacy of our approach in solving inverse problems, such as identifying nonuniform damage distributions within materials. Our proposed approach offers tremendous potential for physics-informed neural networks to solve problems with complex geometries or nonlinearities that require decomposing the computational zone into numerous sub-domains.