Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks

TL;DR

This paper introduces PINN-Proj, a novel projection method for physics-informed neural networks that guarantees adherence to conservation laws, significantly improving their accuracy and physical consistency in solving PDEs.

Contribution

The paper presents PINN-Proj, a new approach that enforces conservation laws in PINNs through a projection method, enhancing physical fidelity and accuracy.

Findings

PINN-Proj outperforms PINN in conserving momentum.

Prediction error reduced by three to four orders of magnitude.

Marginal improvement in state prediction across three PDE datasets.

Abstract

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets.