On learning Hamiltonian systems from data.

Clicks: 319
ID: 78991
2019
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Abstract
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating additional assumptions about the system that generated the data. Here, we propose to explore a particular type of underlying structure in the data: Hamiltonian systems, where an "energy" is conserved. Given a collection of observations of such a Hamiltonian system over time, we extract phase space coordinates and a Hamiltonian function of them that acts as the generator of the system dynamics. The approach employs an autoencoder neural network component to estimate the transformation from observations to the phase space of a Hamiltonian system. An additional neural network component is used to approximate the Hamiltonian function on this constructed space, and the two components are trained jointly. As an alternative approach, we also demonstrate the use of Gaussian processes for the estimation of such a Hamiltonian. After two illustrative examples, we extract an underlying phase space as well as the generating Hamiltonian from a collection of movies of a pendulum. The approach is fully data-driven and does not assume a particular form of the Hamiltonian function.
Reference Key
bertalan2019onchaos Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Bertalan, Tom;Dietrich, Felix;Mezić, Igor;Kevrekidis, Ioannis G;
Journal chaos (woodbury, ny)
Year 2019
DOI
10.1063/1.5128231
URL
Keywords
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