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

Area of Science:

• Computational Physics
• Chemical Physics
• Dynamical Systems Theory

Background:

• Many physical and biological systems exhibit metastable dynamics, involving long periods of stability followed by rapid transitions.
• Accurate quantification of local relaxation and first-escape times is crucial for simulating long-time dynamics in these systems.

Purpose of the Study:

• To extend data-driven Koopman operator methods for analyzing metastable dynamics.
• To incorporate quasi-stationary distributions (QSDs) and absorbing boundary conditions for improved accuracy.

Main Methods:

• Developed an absorbing Koopman formulation by enforcing absorbing boundary conditions on metastable states.
• Applied data-driven techniques to estimate Koopman operators from short trajectory data.

Main Results:

• The absorbing Koopman formulation reliably recovers spectral properties governing relaxation and escape.
• Demonstrated accurate estimation using only short-trajectory data.

Conclusions:

• The proposed method provides a robust way to analyze complex metastable systems.
• Coupling spectral estimates with parallel-in-time simulation schemes significantly extends accessible simulation timescales.