(310e) Efficient Generation of Barrier Crossing Trajectories Using Approximate Brownian Bridges

We examine conditioned continuous random walks which reach one region before another. These conditioned processes are used to efficiently sample rare trajectories for barrier crossing events. The processes are conditioned using a Brownian Bridge construction, resulting in near perfect sampling efficiency without accruing any loss in the conditional statistics of the process. The construction requires the hitting probability or committer function, which is a solution to the Backward Fokker-Planck (BFP) equation, a PDE that can be difficult to solve through general means. Therefore, we derive a 1D analytical approximation using the asymptotic properties of the BFP which approaches the true solution as barrier height increases. Trajectories generated via this approximate bridge are then shown to result in accurate conditional statistics when used in conjunction with importance sampling, even in the case when potential energy barriers are not large. We demonstrate this methodology by simulating rare events in a stochastic chemical reaction network (Schogl reaction) with multiple steady states. This methodology shows great promise for future implementation for simulating rare barrier crossing events for a wide variety of physical processes.