Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems

Elsa Cardoso-Bihlo; Alex Bihlo

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arXiv · 2311.14131

Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems

Elsa Cardoso-Bihlo·Alex Bihlo

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Abstract

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.

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Elsa Cardoso-Bihlo, Alex Bihlo. 2023-11-23. Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems. https://arxiv.org/abs/2311.14131

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