Symplectic Neural Flows for Modeling and Discovery

• URL: http://arxiv.org/abs/2412.16787v1
• Date: Sat, 21 Dec 2024 22:02:00 GMT
• Title: Symplectic Neural Flows for Modeling and Discovery
• Authors: Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb, Ferdia Sherry, Zakhar Shumaylov,
• Abstract summary: SympFlow is a time-dependent symplectic neural network designed using parameterized Hamiltonian flow maps. It allows for backward error analysis and ensures the preservation of the symplectic structure. We demonstrate the effectiveness of SympFlow on diverse problems, including chaotic and dissipative systems.
• Score: 9.786274281068815
• License:
• Abstract: Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose, but neural network-based methods that incorporate these principles remain underexplored. This work introduces SympFlow, a time-dependent symplectic neural network designed using parameterized Hamiltonian flow maps. This design allows for backward error analysis and ensures the preservation of the symplectic structure. SympFlow allows for two key applications: (i) providing a time-continuous symplectic approximation of the exact flow of a Hamiltonian system--purely based on the differential equations it satisfies, and (ii) approximating the flow map of an unknown Hamiltonian system relying on trajectory data. We demonstrate the effectiveness of SympFlow on diverse problems, including chaotic and dissipative systems, showing improved energy conservation compared to general-purpose numerical methods and accurate

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