H-FEX: A symbolic learning method for Hamiltonian systems.

Area of Science:

• Physics
• Applied Mathematics
• Machine Learning

Background:

• Hamiltonian systems are crucial for modeling diverse physical phenomena, governed by energy functions.
• Data-driven methods like symbolic regression can learn dynamical system equations but struggle with complex Hamiltonians and energy conservation.
• Existing approaches often fail to accurately represent intricate interactions within Hamiltonian functions.

Purpose of the Study:

• To introduce the Hamiltonian Finite Expression Method (H-FEX), a novel symbolic learning technique.
• To enhance the accurate recovery of complex Hamiltonian functions from observational data.
• To ensure the preservation of energy conservation in learned models over extended time scales.

Main Methods:

• Developed H-FEX, a symbolic learning approach incorporating novel interaction nodes.
• Designed H-FEX to effectively capture intricate interaction terms in Hamiltonian functions.
• Applied H-FEX to learn governing equations from observational data of Hamiltonian systems.

Main Results:

• H-FEX successfully recovered complex Hamiltonian functions for various systems, including highly stiff ones.
• The method demonstrated accurate capture of system dynamics.
• Energy conservation was preserved over long time horizons, outperforming existing methods.

Conclusions:

• H-FEX offers a powerful framework for discovering closed-form expressions of complex dynamical systems.
• The novel interaction nodes are key to capturing intricate terms and ensuring energy conservation.
• This approach advances data-driven discovery for Hamiltonian mechanics.