  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.
