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

2023/11/23 by Elsa Dos Santos Cardoso‐Bihlo, Cardoso-Bihlo, Elsa, Alex Bihlo +1 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural Networks and Reservoir Computing #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2311.14131

openalex publication_date 2023/11/23 · openalex created_date 2023/11/28 · openalex updated_date 2026/07/28

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.

Cited by

• Physically consistent model learning for reaction-diffusion systems
• Guaranteeing Conservation of Integrals with Projection in Physics-Informed Neural Networks
• Physics-Informed Operator Learning for Hemodynamic Modeling
• Low-rank adaptive physics-informed HyperDeepONets for solving differential equations
• Adaptive Correction for Ensuring Conservation Laws in Neural Operators

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