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  3. On Learning Hamiltonian Systems From Data.
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On learning Hamiltonian systems from data.

Tom Bertalan1, Felix Dietrich2, Igor Mezić3

  • 1Department of Mechanical Engineering, The Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Chaos (Woodbury, N.Y.)
|January 3, 2020

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a data-driven method to uncover hidden structures in data, specifically identifying Hamiltonian systems by extracting conserved energy and dynamics. It enables the discovery of phase space and generating functions from observations.

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Area of Science:

  • Data Science
  • Physics
  • Machine Learning

Background:

  • Scientific descriptions often leverage conserved quantities, but data science typically lacks this.
  • Current data science methods often overlook underlying physical system assumptions.

Purpose of the Study:

  • To develop a data-driven approach for identifying Hamiltonian systems and their properties.
  • To extract phase space coordinates and the generating Hamiltonian function from observational data.

Main Methods:

  • Utilizing an autoencoder neural network to map observations to phase space coordinates.
  • Employing a second neural network to approximate the Hamiltonian function, trained jointly with the autoencoder.
  • Exploring Gaussian processes as an alternative for Hamiltonian estimation.

Main Results:

  • Successfully extracted phase space and generating Hamiltonians from observational data.
  • Demonstrated the approach with two illustrative examples and a pendulum system.
  • The method is fully data-driven, requiring no prior assumptions on the Hamiltonian's form.

Conclusions:

  • This data-driven framework effectively identifies and characterizes Hamiltonian systems.
  • The approach offers a novel way to integrate physical principles into data analysis.
  • Enables the discovery of underlying dynamics and conserved quantities in complex systems.