Search

Many processes in nature such as conformal changes in biomolecules and clusters of interacting particles, genetic switches, noisy mechanical or electromechanical oscillators, and many others are modeled using stochastic differential equations with small white noise. The study of rare transitions between metastable states in such systems is of great interest and importance, but direct simulations are difficult due to long waiting times. Transition path theory is a mathematical framework for the quantitative description of rare events. Its direct implementation the key component of which is the solution of the committor problem, a boundary value problem for the backward Kolmogorov equation, is often challenging due to high dimensionality or other numerical issues. This work exploits the key fact that the optimal controller constructed from the committor leads to generation of transition trajectories exclusively.