Data-Driven Characterization and Acceleration of Metastable Dynamics Using Koopman Operators

Many physical and biological systems evolve through metastable dynamics characterized by long intervals during which the trajectory remains confined to a small region of the configuration space punctuated by rare but rapid transitions between such regions. Accurately quantifying both the local relaxation and the first-escape behavior from each metastable set is central to many applications including enabling the simulation of long-time dynamics. In this work, we extend well-established data-driven methods for estimating Koopman operators to the setting of quasi-stationary distributions (QSDs) by enforcing absorbing boundary conditions on metastable states. We show that this absorbing Koopman formulation reliably recovers the spectral properties governing relaxation and escape using only short-trajectory data. Finally, we show how these spectral estimates naturally couple with a general parallel-in-time simulation scheme, enabling rigorous and substantial extensions of the time scales accessible to direct simulation of complex metastable systems.