Exactly conservative physics-informed neural networks and deep operator
  networks for dynamical systems
Elsa Cardoso-Bihlo Alex Bihlo
We introduce a method for training exactly conservative physics-informed
neural networks and physics-informed deep operator networks for dynamical
systems. The method employs a projection-based technique that maps a candidate
solution learned by the neural network solver for any given dynamical system
possessing at least one first integral onto an invariant manifold. We
illustrate that exactly conservative physics-informed neural network solvers
and physics-informed deep operator networks for dynamical systems vastly
outperform their non-conservative counterparts for several real-world problems
from the mathematical sciences.