  A coupled computational approach to simultaneously learn a vector field and
the region of attraction of an equilibrium point from generated trajectories of
the system is proposed. The nonlinear identification leverages the local
stability information as a prior on the system, effectively endowing the
estimate with this important structural property. In addition, the knowledge of
the region of attraction plays an experiment design role by informing the
selection of initial conditions from which trajectories are generated and by
enabling the use of a Lyapunov function of the system as a regularization term.
Numerical results show that the proposed method allows efficient sampling and
provides an accurate estimate of the dynamics in an inner approximation of its
region of attraction.
