Statistical Mechanics of Histories: A Cluster Monte Carlo Algorithm

We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium system using the path integral approach. We introduce a cluster algorithm that efficiently samples histories and discuss how to include measurements that are available into the estimate of the histories. This allows our approach to be applicable to the simulation of rare events and to optimal state and parameter estimation. We demonstrate the utility of this approach for $\phi^4$ Langevin dynamics in two spatial dimensions where our algorithm improves sampling efficiency up to an order of magnitude.