Learning a reduced basis of dynamical systems using an autoencoder

David Sondak and Pavlos Protopapas
Phys. Rev. E 104, 034202 – Published 3 September 2021

Abstract

Machine learning models have emerged as powerful tools in physics and engineering. In this work, we use an autoencoder with latent space penalization to discover approximate finite-dimensional manifolds of two canonical partial differential equations. We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV), and damped KdV equations. We show that the resulting optimal latent space of the K-S equation is consistent with the dimension of the inertial manifold. We then uncover a nonlinear basis representing the manifold of the latent space for the K-S equation. The results for the KdV equation show that it is more difficult to recover a reduced latent space, which is consistent with the truly infinite-dimensional dynamics of the KdV equation. In the case of the damped KdV equation, we find that the number of active dimensions decreases with increasing damping coefficient.

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  • Received 20 October 2020
  • Revised 28 April 2021
  • Accepted 19 July 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034202

©2021 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary PhysicsGeneral Physics

Authors & Affiliations

David Sondak* and Pavlos Protopapas

  • Institute for Applied Computational Science, Harvard University, Cambridge, Massachusetts 02138, USA

  • *Present address: Dassault Systèmes Simulia Corp., 175 Wyman St, Waltham, MA 02451, USA; david.sondak@3ds.com

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Vol. 104, Iss. 3 — September 2021

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