Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems
This addresses the challenge of preserving physical invariants in machine learning solvers for dynamical systems, which is crucial for accurate simulations in fields like physics and engineering.
The authors tackled the problem of enforcing exact conservation laws in physics-informed neural networks and deep operator networks for dynamical systems, achieving significantly better performance than non-conservative methods on real-world problems.
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.