ADAPTIVE FORCE BIASING ALGORITHMS: NEW CONVERGENCE RESULTS AND TENSOR APPROXIMATIONS OF THE BIAS

• 成果类型: Article
• 署名作者: Ehrlacher, Virginie; Lelievre, Tony; Monmarche, Pierre
• 署名单位: Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1775
• 发表日期: 2022
• 页码: 3850-3888
• 关键词: free-energy calculations; potential methods

摘要

We analyze and propose variants of the adaptive biasing force method. First, we prove the convergence of a version of the algorithm where the biasing force is estimated using a weighted occupation measure, with an explicit asymptotic variance. Second, we propose a new flavour of the algorithm adapted to high-dimensional reaction coordinates, for which the standard approaches suffer from the curse of dimensionality. More precisely, the free energy is approximated by a sum of tensor products of one-dimensional functions. The consistency of the tensor approximation is established. Numerical experiments on five-dimensional reaction coordinates demonstrate that the method is indeed able to capture correlations between them.