  Physics-guided Neural Networks (PGNNs) represent an emerging class of neural
networks that are trained using physics-guided (PG) loss functions (capturing
violations in network outputs with known physics), along with the supervision
contained in data. Existing work in PGNNs has 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 PG functions with competing gradient directions, there
is a need to adaptively tune the contribution of different 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, which is commonly encountered in 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. All the code and data used
in this work is available at https://github.com/jayroxis/Cophy-PGNN.
