Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks

TL;DR

This paper introduces an enhanced discrete physics-informed neural network framework with enforced interface constraints, enabling accurate, stable, and scalable modeling of physical systems through domain decomposition and independent meshing.

Contribution

It proposes a novel EIC mechanism for dPINNs that enforces interface conditions without auxiliary sampling, improving stability and computational flexibility.

Findings

Accurately models physical systems with enforced interface constraints.

Achieves stability and robustness by eliminating weak spatial constraints.

Demonstrates scalability and efficiency in large-scale 2D and 3D problems.

Abstract

This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style mesh discretization, the dPINN accurately evaluates system energy through Gaussian quadrature-based element-wise integration. To ensure physical field continuity across subdomain interfaces, the EIC mechanism enforces interfacial displacement constraints without requiring auxiliary sampling or loss penalties.This formulation supports independent meshing in each subdomain, simplifying preprocessing and improving computational flexibility. Additionally, by eliminating the influence of weak spatial constraints (WSC) commonly observed in traditional PINNs, the EIC-dPINN delivers more stable and physically consistent predictions.Extensive two- and three-dimensional numerical experiments validate the proposed framework's accuracy and demonstrate the computational efficiency gains achieved through parallel training. The results highlight the framework's scalability, robustness, and potential for solving large-scale, geometrically complex problems.