Adaptive sampling of large deviations

TL;DR

This paper presents an adaptive algorithm for estimating large deviation functions in Markov processes, improving the efficiency of rare event sampling in nonequilibrium systems.

Contribution

It introduces a novel adaptive sampling algorithm that estimates large deviation functions using a driven process, enhancing importance sampling for stochastic fluctuations.

Findings

The algorithm accurately estimates large deviation functions from a single trajectory.

It outperforms traditional methods like splitting or cloning in efficiency.

Demonstrated effectiveness on equilibrium and nonequilibrium diffusion models.

Abstract

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting the probability and pathways of rare events in stochastic processes, as well as for understanding the physics of nonequilibrium systems driven in steady states by external forces and reservoirs. The algorithm uses methods from risk-sensitive and feedback control to estimate from a single trajectory a new process, called the driven process, known to be efficient for importance sampling. Its advantages compared to other simulation techniques, such as splitting or cloning, are discussed and illustrated with simple equilibrium and nonequilibrium diffusion models.