Learning dominant physical processes with data-driven balance models

Jared L. Callaham (), James V. Koch, Bingni W. Brunton, J. Nathan Kutz and Steven L. Brunton
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Jared L. Callaham: University of Washington
James V. Koch: University of Texas
Bingni W. Brunton: University of Washington
J. Nathan Kutz: University of Washington
Steven L. Brunton: University of Washington

Nature Communications, 2021, vol. 12, issue 1, 1-10

Abstract: Abstract Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

Date: 2021
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DOI: 10.1038/s41467-021-21331-z

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