H-FEX: A Symbolic Learning Method for Hamiltonian Systems

TL;DR

H-FEX is a symbolic learning approach that effectively captures complex Hamiltonian functions from data, accurately modeling system dynamics and energy conservation in stiff and intricate systems.

Contribution

The paper introduces H-FEX, a novel symbolic learning method with specialized interaction nodes for better modeling complex Hamiltonian systems from observational data.

Findings

H-FEX accurately recovers Hamiltonian functions of complex systems.

H-FEX preserves energy over long-term simulations.

H-FEX outperforms existing methods on stiff dynamical systems.

Abstract

Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural network-based methods, provide a means to learn the governing equations of dynamical systems directly from observational data of Hamiltonian systems. However, these methods often struggle to accurately capture complex Hamiltonian functions while preserving energy conservation. To overcome this limitation, we propose the Finite Expression Method for learning Hamiltonian Systems (H-FEX), a symbolic learning method that introduces novel interaction nodes designed to capture intricate interaction terms effectively. Our experiments, including those on highly stiff dynamical systems, demonstrate that H-FEX can recover Hamiltonian functions of complex systems that accurately capture system dynamics and preserve energy over long time horizons. These findings highlight the potential of H-FEX as a powerful framework for discovering closed-form expressions of complex dynamical systems.