Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations
Creators
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1.
California Institute of Technology
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2.
Massachusetts Institute of Technology
Abstract
Despite rapid progress in data acquisition techniques, many complex physical, chemical, and biological systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an incomplete set of experimentally accessible time series. Here, we combine sensitivity methods and ranked-choice model selection to construct an automated hidden dynamics inference framework that can discover predictive nonlinear dynamical models for both observable and latent variables from noise-corrupted incomplete data in oscillatory and chaotic systems. After validating the framework for prototypical FitzHugh-Nagumo oscillations, we demonstrate its applicability to experimental data from squid neuron activity measurements and Belousov-Zhabotinsky reactions, as well as to the Lorenz system in the chaotic regime. Published by the American Physical Society 2024
Copyright and License
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.
Acknowledgement
We thank Keaton Burns and Peter Baddoo for helpful discussions on partially observed systems. We acknowledge the MIT SuperCloud and Lincoln Laboratory Supercomputing Center [120] for providing HPC resources. J.F.T. acknowledges support through a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation. G.S. acknowledges support through a National Science Foundation Graduate Research Fellowship under Grant No. 1745302. This work was supported by a MathWorks Science Fellowship (A.D.H.), Sloan Foundation Grant G-2021-16758 (J.D.), and the Robert E. Collins Distinguished Scholarship Fund (J.D.). This research received support through Schmidt Sciences, LLC (Schmidt Science Polymath Award to J.D.).
Contributions
G.S. and A.D.H. contributed equally and are joint first authors.
Supplemental Material
- supplementary.pdf: Supplementary material detailing the entire HDI framework, extended computational experiments, as well as specifics of experiments and datasets for reproducibility.
- SI_movie.mp4: Movie of four Belousov-Zhabotinsky chemical reactions and the model fit trajectories.
Files
PhysRevResearch.6.043062.pdf
Additional details
Funding
- Alexander von Humboldt Foundation
- National Science Foundation
- Graduate Research Fellowship 1745302
- Alfred P. Sloan Foundation
- G-2021-16758
- MathWorks (United States)
- Science Fellowship -
Dates
- Accepted
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2024-09-21Accepted
- Available
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2024-10-23Published online
Caltech Custom Metadata
- Publication Status
- Published