(103a) Brownian Bridges for Stochastic Chemical Processes – Applications and Approximation Method

A Brownian bridge is a continuous random walk conditioned to end in a given region of phase space. This phenomenon has many applications in chemical science where one wants to control the endpoint of a stochastic process – e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of generating a Brownian bridge is that one needs to compute a drift that guides the random path to the end region with the correct statistics. This drift arises from the entropic penalty in constraining the random walk, and is derived from a Backwards Fokker Planck (BFP) equation that is infeasible to compute for complex systems. This talk introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, the talk will use the asymptotic properties of the BFP equation to generate an approximate drift, and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of BFP equation, we show that it drastically accelerates the generation of conditioned random walks and allows the generation of such processes to be scaled to higher dimensions and complex systems. We will also show that this approach offers reasonable improvement compared to other importance sampling methods that use simple bias potentials.