Active learning attraction basins of dynamical system

Dynamical systems often exhibit multiple attractors representing significantly different functioning conditions. A global map of attraction basins can offer valuable guidance for stabilizing or transitioning system states. Such a map can be constructed without prior system knowledge by identifying attractors across a sufficient number of points in the state space. However, determining the attractor for each initial state can be a laborious task. Here, we tackle the challenge of reconstructing attraction basins using as few initial points as possible. In each iteration of our approach, informative points are selected through random seeding and are driven along the current classification boundary, promoting the eventual selection of points that are both diverse and enlightening. The results across various experimental dynamical systems demonstrate that our approach requires fewer points than baseline methods while achieving comparable mapping accuracy. Additionally, the reconstructed map allows us to accurately estimate the minimum escape distance required to transition the system state to a target basin.