Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks

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 created PINN-Proj, a PINN-based model which uses a novel projection method to enforce to conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and guaranteed conservation to an accuracy of while performing marginally better in the separate task of state prediction on three PDE datasets.