  Learning governing equations from a family of data sets which share the same
physical 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 data
sets as well as the range of parameter values. On the other hand, it is common
to assume only a small number of candidate functions contribute to the observed
dynamics. Based on these observations, we propose a group-sparse penalized
method for model selection and parameter estimation for such data. We also
provide convergence guarantees for our proposed numerical scheme. Various
numerical experiments including the 1D logistic equation, the 3D Lorenz sampled
from different bifurcation regions, and a switching system provide numerical
validation for our method and suggest potential applications to applied
dynamical systems.
