Data-driven analysis of metastability in a stochastic bistable system

TL;DR

This paper introduces a data-driven Koopman operator approach to analyze metastability in bistable systems, accurately capturing escape dynamics and basin structures without relying on trajectory tracking.

Contribution

It presents a novel Koopman-based framework for studying metastability, providing insights into escape times and basin reconstruction in both equilibrium and nonequilibrium conditions.

Findings

Agrees with large deviation theory predictions for escape times.

Accurately reconstructs basins of attraction.

Identifies modes related to intrawell variability and escape dynamics.

Abstract

We study the metastability properties of a simple prototypical bistable system 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. We find agreement with the predictions - both the exponential and subexponential ones - of large deviation theory in the weak-noise limit for the statistics of escape time, both in equilibrium and nonequilibrium conditions. The subdominant Koopman mode also allows for an accurate reconstruction of the competing basins of attraction. Going deeper in the Koopman spectrum, we are able to recognise modes that are associated with intrawell variability as well as with the escape of trajectories from the saddle towards the attractor, both in the equilibrium and nonequilibrium case. Our methodology, being grounded in purely data-driven techniques, could be helpful for studying high-dimensional metastable systems.