Learning physics-guided neural networks with competing physics loss: A summary of results in solving eigenvalue problems

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. However, 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 during 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 approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation.