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This study introduces an absorbing Koopman operator method to analyze metastable dynamics. It accurately quantifies system relaxation and escape behavior from short trajectory data, enabling longer simulations.

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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.