Learning Symmetries of Classical Integrable Systems

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.

8 pages, 5 figures. Presented at the ICML 2019 Workshop on Theoretical Physics for Deep Learning

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Cited by in corpus (11)

• Hamiltonian Neural Networks
• AI Poincaré: Machine Learning Conservation Laws from Trajectories
• Physics enhanced neural networks predict order and chaos
• Neural Canonical Transformation with Symplectic Flows
• Locally-symplectic neural networks for learning volume-preserving dynamics
• Learning Group Structure and Disentangled Representations of Dynamical Environments
• Learning Potentials of Quantum Systems using Deep Neural Networks
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning
• SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
• Time-Reversal Symmetric ODE Network
• Discovering Symmetries of ODEs by Symbolic Regression