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Discovering the governing laws underpinning physical and chemical phenomenais a key step towards understanding and ultimately controlling systems inscience and engineering. We introduce Discovery of Dynamical Systems via MovingHorizon Optimization (DySMHO), a scalable machine learning framework foridentifying governing laws in the form of differential equations fromlarge-scale noisy experimental data sets. DySMHO consists of a novel movinghorizon dynamic optimization strategy that sequentially learns the underlyinggoverning equations from a large dictionary of basis functions. The sequentialnature of DySMHO allows leveraging statistical arguments for eliminatingirrelevant basis functions, avoiding overfitting to recover accurate andparsimonious forms of the governing equations. Canonical nonlinear dynamicalsystem examples are used to demonstrate that DySMHO can accurately recover thegoverning laws, is robust to high levels of measurement noise and that it canhandle challenges such as multiple time scale dynamics.

DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization