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  • Featured in Physics
  • Letter
  • Open Access

Data-driven discovery and extrapolation of parameterized pattern-forming dynamics

Zachary G. Nicolaou1, Guanyu Huo1, Yihui Chen1, Steven L. Brunton2, and J. Nathan Kutz1

  • 1Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
  • 2Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195, USA

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Phys. Rev. Research 5, L042017 – Published 2 November, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042017

Abstract

Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying transitions can be characterized using bifurcation theory on model systems whose governing equations are known. In contrast, data-driven methods for more complicated and realistic systems whose governing evolution dynamics are unknown have only recently been developed. Here, we develop a data-driven approach, the sparse identification for nonlinear dynamics with control parameters (SINDyCP), to discover dynamics for systems with adjustable control parameters, such as an external driving strength. We demonstrate the method on systems of varying complexity, ranging from discrete maps to systems of partial differential equations. To mitigate the impact of measurement noise, we also develop a weak formulation of SINDyCP and assess its performance on noisy data. We demonstrate applications including the discovery of universal pattern-formation equations, and their bifurcation dependencies, directly from data accessible from experiments and the extrapolation of predictions beyond the weakly nonlinear regime near the onset of an instability.

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Research News

Learning Governing Equations and Control Parameters from Data

Published 2 November, 2023

Using a few measurements of a pattern-forming system, a new machine-learning algorithm can determine the system’s governing equations and their parameters in a form that is interpretable by scientists.

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References (45)

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Outline

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Phys. Rev. Research 5, L042017– Published 2 November, 2023
  • Received 24 January 2023
  • Accepted 13 September 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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