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Learning governing equations from a family of data sets which share the samephysical laws but differ in bifurcation parameters is challenging. This is due,in part, to the wide range of phenomena that could be represented in the datasets as well as the range of parameter values. On the other hand, it is commonto assume only a small number of candidate functions contribute to the observeddynamics. Based on these observations, we propose a group-sparse penalizedmethod for model selection and parameter estimation for such data. We alsoprovide convergence guarantees for our proposed numerical scheme. Variousnumerical experiments including the 1D logistic equation, the 3D Lorenz sampledfrom different bifurcation regions, and a switching system provide numericalvalidation for our method and suggest potential applications to applieddynamical systems.

Learning Dynamical Systems and Bifurcation via Group Sparsity