Sparse identification of nonlinear dynamics for rapid model recovery

  • Big data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on severalBig data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change. In this work, we propose a conceptual framework to recover parsimonious models of a system in response to abrupt changes in the low-data limit. First, the abrupt change is detected by comparing the estimated Lyapunov time of the data with the model prediction. Next, we apply the sparse identification of nonlinear dynamics (SINDy) regression to update a previously identified model with the fewest changes, either by addition, deletion, or modification of existing model terms. We demonstrate this sparse model recovery on several examples for abrupt system change detection in periodic and chaotic dynamical systems. Our examples show that sparse updates to a previously identified model perform better with less data, have lower runtime complexity, and are less sensitive to noise than identifying an entirely new model. The proposed abrupt-SINDy architecture provides a new paradigm for the rapid and efficient recovery of a system model after abrupt changes.show moreshow less

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author details:Markus QuadeORCiD, Markus AbelORCiDGND, J. Nathan Kutz, Steven L. BruntonORCiD
DOI:https://doi.org/10.1063/1.5027470
ISSN:1054-1500
ISSN:1089-7682
Pubmed ID:http://www.ncbi.nlm.nih.gov/pubmed?term=29960401
Title of parent work (English):Chaos : an interdisciplinary journal of nonlinear science
Publisher:American Institute of Physics
Place of publishing:Melville
Publication type:Article
Language:English
Date of first publication:2018/06/18
Completion year:2018
Release date:2021/11/25
Volume:28
Issue:6
Number of pages:10
Funding institution:FITweltweit program of the German Academic Exchange Service (DAAD)Deutscher Akademischer Austausch Dienst (DAAD); European Erasmus SME/HPC project [588372-EPP-1-2017-1-IE-EPPKA2-KA]; DARPAUnited States Department of DefenseDefense Advanced Research Projects Agency (DARPA) [HR0011-16-C-0016]; ARO Young Investigator Program [ARO W911NF-17-1-0422]; AFOSR Young Investigator Program [AFOSR FA9550-18-10200]
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access