Learning dominant physical processes with data-driven balance models

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.

arXiv comment30 pages, 13 figures

References in corpus (12)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Turbulence Modeling in the Age of Data
• A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence
• Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
• Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection
• Scaling of the turbulence transition threshold in a pipe
• Elasto-inertial turbulence
• Data-assisted reduced-order modeling of extreme events in complex dynamical systems
• Resolvent-analysis-based design of airfoil separation control
• Multiscale polar theory of microtubule and motor-protein assemblies
• Learning dominant physical processes with data-driven balance models
• Mode-Locked Rotating Detonation Waves: Experiments and a Model Equation

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