  Governing equations are essential to the study of nonlinear dynamics, often
enabling the prediction of previously unseen behaviors as well as the inclusion
into control strategies. The discovery of governing equations from data thus
has the potential to transform data-rich fields where well-established
dynamical models remain unknown. This work contributes to the recent trend in
data-driven sparse identification of nonlinear dynamics of finding the best
sparse fit to observational data in a large library of potential nonlinear
models. We propose an efficient first-order Conditional Gradient algorithm for
solving the underlying optimization problem. In comparison to the most
prominent alternative algorithms, the new algorithm shows significantly
improved performance on several essential issues like sparsity-induction,
structure-preservation, noise robustness, and sample efficiency. We demonstrate
these advantages on several dynamics from the field of synchronization,
particle dynamics, and enzyme chemistry.
