Discrete physics-informed neural network with enforced interface constraint for domain decomposition

Abstract

While domain decomposition method (DDM) constitutes an effective strategy for improving the training efficiency of physics-informed neural network (PINN), the approach simultaneously introduces an increased risk of training instability owing to the additional loss terms introduced. To address this issue, the work proposes an energy-based discrete PINN (dPINN) approach incorporating a proposed enforced interface constraint (EIC) mechanism within the context of the DDM. The dPINN builds upon the DDM with the EIC mechanism and will henceforth be referred to as EIC-DDM-dPINN. Within this framework, the dPINN computes the system energy in an element-wise fashion using Gaussian integration, guided by finite element-inspired formulations. Meanwhile, displacement continuity across subdomain interfaces is explicitly enforced through the EIC mechanism. This enforcement obviates the need to incorporate supplementary loss terms into the loss function, thereby substantially mitigating the risk of training instability. The integration of the EIC-based DDM facilitates simpler and more flexible subdomain mesh partitioning within the EIC-DDM-dPINN framework, thereby reducing the strong dependence on sampling strategies typically required in conventional DDM-based PINN. Beyond improving computational efficiency via parallelization, the DDM also helps decouple the weak spatial constraint (WSC) effect, which can otherwise result in spurious displacement continuity across geometrically discontinuous gaps. Comprehensive numerical experiments in both two- and three-dimensional settings are conducted to assess the accuracy and efficiency of the proposed approach, and the results demonstrate its scalability and robustness, highlighting its potential for application to large-scale problems with complex geometries.