(525e) Efficient Simulation of Rare-Events Using Approximate Brownian Bridges

The simulation of rare events is an important problem in chemical physics with numerous challenges and applications. To investigate such phenomena, we study a process known as a generalized Brownian bridge – i.e., a continuous random walk conditioned to lie in a specified region of phase space and/or end in a given region. This random process has broad applicability when one wants to control the endpoint of stochastic systems, which is often the case in fields like polymer physics and reaction systems. However, construction of a bridge requires solving a Backwards Fokker-Planck (BFP) equation which suffers from the “Curse of Dimensionality” and thus is impractical to compute on complex and high dimensional potential energy surfaces. Therefore, we propose leveraging approximate solutions in conjunction with an importance sampling scheme to correct (re-weight) any errors which occur. Specifically, we efficiently generate rare-events such as barrier-crossing trajectories and trajectories which stay within a region of phase-space for a long time by exploiting the asymptotic properties of the BFP and leveraging the systems dependence on the dominant eigenvalue at large times respectively. We see that these approximations drastically simplify the bridge construction while maintaining the statistical accuracy of its results. We will also compare the results of this methodology to other techniques and comment on applications where the Brownian Bridge methodology would be advantageous.