Data-driven analysis of metastability in a stochastic bistable system

We present a methodology to analyze metastable properties of a simple prototypical stochastic bistable system by identifying slow inter-well and fast saddle escape processes using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying the time evolution and the decay rate of the subdominant mode of the Koopman operator, thus in a geometry-agnostic framework. The obtained escape time statistics together with the decay rate are in good agreement with the predictions-both the exponential and subexponential ones-of large deviation theory in the weak-noise limit, both in equilibrium and nonequilibrium conditions. The subdominant Koopman mode also allows for an accurate reconstruction of the competing basins of attraction. Furthermore, going deeper in the Koopman spectrum, we are able to recognize modes that are associated with intra-well variability as well as with the escape of trajectories from the saddle toward the attractor, both in the equilibrium and nonequilibrium case. Our methodology, being grounded in purely data-driven techniques, could provide a comprehensive, multi-scale framework for studying high-dimensional metastable systems.