Improving physics-informed DeepONets with hard constraints
Rüdiger Brecht Dmytro R. Popovych Alex Bihlo Roman O. Popovych
Current physics-informed (standard or operator) neural networks still rely on
accurately learning the initial conditions of the system they are solving. In
contrast, standard numerical methods evolve such initial conditions without
needing to learn these. In this study, we propose to improve current
physics-informed deep learning strategies such that initial conditions do not
need to be learned and are represented exactly in the predicted solution.
Moreover, this method guarantees that when a DeepONet is applied multiple times
to time step a solution, the resulting function is continuous.