Paper ID: 2410.17445

Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks

Anthony Baez, Wang Zhang, Ziwen Ma, Subhro Das, Lam M. Nguyen, Luca Daniel

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.

Submitted: Oct 22, 2024