Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection

TL;DR

This paper introduces an improved adaptive biasing force method that employs Helmholtz projection to reduce variance, leading to faster convergence and increased efficiency in estimating mean forces.

Contribution

The paper presents a novel projection technique for the ABF method, providing theoretical proof of exponential convergence and demonstrating variance reduction through numerical examples.

Findings

Variance of the mean force estimate is reduced.

The method achieves exponential convergence to the stationary state.

Numerical results show improved efficiency over standard ABF.

Abstract

In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. The associated stochastic process satisfies a non linear stochastic differential equation. Using entropy techniques, we prove exponential convergence to the stationary state of this stochastic process. We finally show on some numerical examples that the variance of the approximated mean force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method.