Symplectic Neural Networks Based on Dynamical Systems

2024/08/19 by Benjamin K. Tapley, Tapley, Benjamin K · 1 citation
Computer Science · #Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Machine Learning (cs.LG) #Neural Networks and Applications #Neural Networks and Reservoir Computing #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · pdf · doi:10.48550/arxiv.2408.09821

openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interpretable and have a non-vanishing gradient property. We also give a representation theory for linear systems, meaning the proposed P-SympNets can exactly parameterize any symplectic map corresponding to quadratic Hamiltonians. Extensive numerical tests demonstrate increased expressiveness and accuracy -- often several orders of magnitude better -- for lower training cost over existing architectures. Lastly, we show how to perform symbolic Hamiltonian regression with SympNets for polynomial systems using backward error analysis.

Cited by

• Neural non-canonical Hamiltonian dynamics for long-time simulations

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