Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks
This addresses the issue of ensuring conservation laws in PINNs for physical system modeling, but it is incremental as it builds on existing PINN methods.
The paper tackled the problem of physics-informed neural networks (PINNs) failing to guarantee adherence to conservation laws in modeling physical systems, and the result was that PINN-Proj substantially outperformed PINN by lowering prediction error by three to four orders of magnitude and conserving momentum better.
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.