An Optimal Control Approach to Efficient Estimation of Rare Event Statistics

Christof Schuette
Freie Universität Berlin

Driven by progress in experimental techniques to manipulate single molecules, nonequilibrium simulation methods for estimating equilibrium expectation values, like the methods based on the Jarzynski/Crooks identities, have gained enormous popularity. However, in most cases the respective statistical estimators suffer from slow convergence due to large variance.
In this talk some new results are discussed that allow for the construction of zero or very low variance estimators.
These results are based on the insight that certain equilibrium expectation values can be equivalently expressed in terms of (1) the solution of certain stochastic optimal control problem, and simultaneously as (2) optimal change of measure problems. This insight allows for designing low variance estimators for equilibrium quantities (such as transition rates) by using optimal protocols, the downside being that one has to solve an optimal control or change of measure problem. We will discuss how this can be done efficiently and demonstrate the performance of the resulting algorithms for computing rare events in molecular systems.

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