Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias

TL;DR

This paper introduces an improved adaptive biasing force algorithm that uses tensor product approximations to handle multiple reaction coordinates, with proven convergence and demonstrated ability to capture coordinate correlations.

Contribution

It presents a novel tensor-based modification of the adaptive biasing force method, enabling efficient handling of many reaction coordinates and providing convergence proofs.

Findings

Algorithm converges to a regularized free energy

Method captures correlations between reaction coordinates

Numerical experiments validate effectiveness

Abstract

A modification of the Adaptive Biasing Force method is introduced, in which the free energy is approximated by a sum of tensor products of one-dimensional functions. This enables to handle a larger number of reaction coordinates than the classical algorithm. We prove the algorithm is well-defined and prove the long-time convergence toward a regularized version of the free energy for an idealized version of the algorithm. Numerical experiments demonstrate that the method is able to capture correlations between reaction coordinates.