Identifying Physical Law of Hamiltonian Systems via Meta-Learning

TL;DR

This paper introduces a meta-learning approach to identify the underlying physical laws in Hamiltonian systems from observational data, eliminating the need for prior mathematical assumptions and expert-designed experiments.

Contribution

It demonstrates that meta-learning algorithms can effectively discover the shared Hamiltonian representation across different physical systems without predefined mathematical forms.

Findings

Meta-learning can identify Hamiltonians from observational data.

The method works across various physical systems and experimental setups.

It reduces reliance on expert knowledge and predefined assumptions.

Abstract

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related phenomena that are governed by the same physical law. However, in general, identifying a functional or shared expression of the Hamiltonian is very difficult. It requires carefully designed experiments and the researcher's insight that comes from years of experience. We propose that meta-learning algorithms can be potentially powerful data-driven tools for identifying the physical law governing Hamiltonian systems without any mathematical assumptions on the representation, but with observations from a set of systems governed by the same physical law. We show that a well meta-trained learner can identify the shared representation of the Hamiltonian by evaluating our method on several types of physical systems with various experimental settings.