Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
File(s)
Published version
Author(s)
Fasel, U
Kutz, JN
Brunton, BW
Brunton, SL
Type
Journal Article
Abstract
Sparse model identification enables the discovery of nonlinear dynamical systems purely from data; however, this approach is sensitive to noise, especially in the low-data limit. In this work, we leverage the statistical approach of bootstrap aggregating (bagging) to robustify the sparse identification of the nonlinear dynamics (SINDy) algorithm. First, an ensemble of SINDy models is identified from subsets of limited and noisy data. The aggregate model statistics are then used to produce inclusion probabilities of the candidate functions, which enables uncertainty quantification and probabilistic forecasts. We apply this ensemble-SINDy (E-SINDy) algorithm to several synthetic and real-world datasets and demonstrate substantial improvements to the accuracy and robustness of model discovery from extremely noisy and limited data. For example, E-SINDy uncovers partial differential equations models from data with more than twice as much measurement noise as has been previously reported. Similarly, E-SINDy learns the Lotka Volterra dynamics from remarkably limited data of yearly lynx and hare pelts collected from 1900 to 1920. E-SINDy is computationally efficient, with similar scaling as standard SINDy. Finally, we show that ensemble statistics from E-SINDy can be exploited for active learning and improved model predictive control.
Date Issued
2022-04
Date Acceptance
2022-03-10
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, 478 (2260), pp.1-20
ISSN
1364-5021
Publisher
The Royal Society
Start Page
1
End Page
20
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
478
Issue
2260
Copyright Statement
© 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.
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.
License URL
Identifier
https://royalsocietypublishing.org/doi/10.1098/rspa.2021.0904
Subjects
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2022-04-13