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Governing equations are essential to the study of nonlinear dynamics, oftenenabling the prediction of previously unseen behaviors as well as the inclusioninto control strategies. The discovery of governing equations from data thushas the potential to transform data-rich fields where well-establisheddynamical models remain unknown. This work contributes to the recent trend indata-driven sparse identification of nonlinear dynamics of finding the bestsparse fit to observational data in a large library of potential nonlinearmodels. We propose an efficient first-order Conditional Gradient algorithm forsolving the underlying optimization problem. In comparison to the mostprominent alternative algorithms, the new algorithm shows significantlyimproved performance on several essential issues like sparsity-induction,structure-preservation, noise robustness, and sample efficiency. We demonstratethese advantages on several dynamics from the field of synchronization,particle dynamics, and enzyme chemistry.

CINDy: Conditional gradient-based Identification of Non-linear Dynamics -- Noise-robust recovery