Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection
For researchers using molecular dynamics simulations, this provides a more efficient ABF method with reduced variance.
The paper improves the adaptive biasing force method by projecting the estimated mean force onto a gradient, proving exponential convergence via entropy techniques and demonstrating variance reduction in numerical examples.
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.