A Koopman framework for rare event simulation in stochastic differential equations

Benjamin J. Zhang, Tuhin Sahai, Youssef M. Marzouk

Abstract: Highlights•We develop a systematic framework for computing rare event probabilities in stochastic differential equations.•Stochastic Koopman eigenfunctions are used to develop importance sampling estimators.•Stochastic Koopman eigenfunctions are computed using dynamic mode decomposition.•Non-rare trajectories are used to inform how rare events occur.•Even crude approximations of eigenfunctions can yield efficient estimators.