Symplectic Neural Networks Based on Dynamical Systems

• URL: http://arxiv.org/abs/2408.09821v1
• Date: Mon, 19 Aug 2024 09:18:28 GMT
• Title: Symplectic Neural Networks Based on Dynamical Systems
• Authors: Benjamin K Tapley,
• Abstract summary: We present and analyze a framework for Symplectic neural networks (SympNets) based on geometric for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interpretable and have a non-vanishing property.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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