Identifying Physical Law of Hamiltonian Systems via Meta-Learning
This work addresses the challenge of automating Hamiltonian identification for researchers in physics and related fields, offering a data-driven alternative to traditional methods, though it appears incremental as it applies existing meta-learning techniques to this specific domain.
The paper tackles the problem of identifying the physical law governing Hamiltonian systems, which is typically difficult and requires expert insight, by proposing a meta-learning approach that can identify shared Hamiltonian representations from observations without mathematical assumptions, achieving successful identification across various physical systems and experimental settings.
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.