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

2020/07/20 by Virginie Ehrlacher, Tony Lelièvre, Ehrlacher, Virginie +3
Computer Science · Mathematics · #65C05 #65N12 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #cs.NA #math.NA #math.PR #msc:65C05 #msc:65N12

paper · pdf · doi:10.48550/arxiv.2007.09941

arxiv created 2020/07/20 · arxiv updated 2020/07/21

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.

Related

• Long-time convergence of an Adaptive Biasing Force method: the bi-channel case
• Analysis of an Adaptive Biasing Force method based on self-interacting dynamics
• The Adaptive Biasing Force algorithm with non-conservative forces and related topics
• Free energy calculations: An efficient adaptive biasing potential method
• Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection