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 [6]. 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.