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Learning dominant physical processes with data-driven balance models

Jared L Callaham, James V Koch, Bingni W Brunton, J Nathan Kutz, Steven L Brunton
2021 Nature Communications  
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
more » ... 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.
doi:10.1038/s41467-021-21331-z pmid:33589607 fatcat:mvpsgama6za6xipjefh5sv42bq