Learning Symmetries of Classical Integrable Systems

2019/06/11 by Roberto Bondesan, Bondesan, Roberto, Austen Lamacraft +1 · 2 citations
Computer Science · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Neural Networks and Applications #Topic Modeling

paper · pdf · doi:10.48550/arxiv.1906.04645

openalex publication_date 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel network architectures that parametrize symplectic transformations. We demonstrate the utility of these architectures by learning the structure of integrable models. Our work exemplifies the adaptation of neural transformations to a family constrained by more than the condition of invertibility, which we expect to be a common feature of applications of these methods.

Citations

• Geometric Deep Learning: Going beyond Euclidean data
• Glow: Generative Flow with Invertible 1x1 Convolutions
• Towards a Definition of Disentangled Representations
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport

Cited by

• Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AI
• Discovering Symmetries of ODEs by Symbolic Regression

Related

• Learning reversible symplectic dynamics
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• Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks
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