Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published April 2022 | Submitted + Supplemental Material + Published
Journal Article Open

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization


Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modelling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. By contrast, sparse identification of nonlinear dynamics learns fully nonlinear models, disambiguating the linear and nonlinear effects, but is restricted to low-dimensional systems. In this work, we present a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems. Our method performs kernel regression on a sparse dictionary of samples that appreciably contribute to the dynamics. We show that this kernel method efficiently handles high-dimensional data and is flexible enough to incorporate partial knowledge of system physics. It is possible to recover the linear model contribution with this approach, thus separating the effects of the implicitly defined nonlinear terms. We demonstrate our approach on data from a range of nonlinear ordinary and partial differential equations. This framework can be used for many practical engineering tasks such as model order reduction, diagnostics, prediction, control and discovery of governing laws.

Additional Information

© 2022 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Manuscript received 28/10/2021. Manuscript accepted 28/02/2022. Published online 13/04/2022. Published in print 27/04/2022. S.L.B. would like to thank Bing Brunton, Nathan Kutz, Jean-Christophe Loiseau and Isabel Scherl for valuable discussions. This work was supported by U.S. Army Research Office (ARO W911NF-17-1-0306 and ARO W911NF-19-1-0045), the U.S. Office of Naval Research (ONR N00014-17-1-3022) and by the PRIME programme of the German Academic Exchange Service (DAAD) with funds from the German Federal Ministry of Education and Research (BMBF). Data accessibility. Further information is provided in the electronic supplementary material [73]. Data and codes are available at www.github.com/baddoo/LANDO. Authors' contributions. P.J.B.: conceptualization, formal analysis, investigation, methodology, visualization, writing–original draft, writing—review and editing; B.H.: methodology, writing—original draft, writing—review and editing; B.J.M.: conceptualization, funding acquisition, supervision, writing—original draft, writing—review and editing; S.L.B.: conceptualization, funding acquisition, methodology, supervision, visualization, writing—original draft, writing—review and editing. All authors gave final approval for publication and agreed to be held accountable for the work performed therein. We declare we have no competing interests.

Attached Files

Published - rspa.2021.0830.pdf

Submitted - 2106.01510.pdf

Supplemental Material - rspa20210830_si_001.pdf


Files (6.4 MB)
Name Size Download all
1.2 MB Preview Download
3.6 MB Preview Download
1.7 MB Preview Download

Additional details

August 22, 2023
October 23, 2023