Learning Physics-guided Neural Networks with Competing Physics Loss: A Summary of Results in Solving Eigenvalue Problems

Anuj Karpatne 

Abstract

Existing work in Physics-guided Neural Networks (PGNNs) have demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. How- ever, in the presence of multiple physics loss functions with competing gradient directions, there is a need to adaptively tune the contribution of competing PG loss functions dur- ing the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, common to many scientific problems. We present a novel ap- proach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivat- ing applications of quantum mechanics and electromagnetic propagation.

Mohannad Elhamod, Jie Bu, Christopher Singh, Matthew Redell, Abantika Ghosh, Viktor Podolskiy, Wei-Cheng Lee, Anuj Karpatne: Learning Physics-guided Neural Networks with Competing Physics Loss: A Summary of Results in Solving Eigenvalue Problems. AAAI Spring Symposium: MLPS 2021