(501f) Brownian Bridge Method for Studying Rare Events – an Approximation Scheme
AIChE Annual Meeting
2021 Annual Meeting
Computational Molecular Science and Engineering Forum
Practical Applications of Computational Chemistry and Molecular Simulation II
Wednesday, November 10, 2021 - 2:00pm to 2:15pm
In this work, an approximation method will be developed to extend the stochastic bridge formalism to more complex systems and higher dimensional problems. In our past work , a stochastic bridge was created by calculating a drift that constrained random walks to the correct regions of phase space. This drift was determined by a solution of a Backwards Fokker Planck (BFK) equation, which is infeasible for complicated systems. We will show how to systematically generate approximations to the drift without solving the BFK equation, and how to correct (i.e., re-weight) any errors incurred from this approximation.
Using asymptotic properties of the Backwards Fokker Planck equation for different applications, we will develop approximations for the hitting probability needed to develop a stochastic bridge. We will then develop a novel procedure to reweight the approximations so that one is guaranteed to generate the correct conditional statistics. We accomplish this goal by applying the approximation method to one dimensional Wiener processes (i.e. Ornstein Ulenbeck process and Geometric Brownian motion). Next, the approach will be generalized for high dimensional systems. The main outcome of this talk will be to show that one can now generate a stochastic bridge without knowing the solution to a high dimensional Fokker Planck equation, which will allow one to apply this methodology to a wide range of problems. We outline many applications that will be served by this development.
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