Identifying Physical Law of Hamiltonian Systems via Meta-Learning

Seungjun Lee, Haesang Yang, Woojae Seong

Keywords: Learning physical laws, meta-learning, Hamiltonian systems

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.

One-sentence Summary: We introduce meta-learning algorithms to identify the shared representation of Hamiltonian systems.

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