Analysis of an Adaptive Biasing Force method based on self-interacting dynamics

Abstract : This article fills a gap in the mathematical analysis of Adaptive Biasing algorithms, which are extensively used in molecular dynamics computations. Given a reaction coordinate, ideally, the bias in the overdamped Langevin dynamics would be given by the gradient of the associated free energy function, which is unknown. We consider an adaptive biased version of the overdamped dynamics, where the bias depends on the past of the trajectory and is designed to approximate the free energy. The main result of this article is the consistency and efficiency of this approach. More precisely we prove the almost sure convergence of the bias as time goes to infinity, and that the limit is close to the ideal bias, as an auxiliary parameter of the algorithm goes to 0. The proof is based on interpreting the process as a self-interacting dynamics, and on the study of a non-trivial fixed point problem for the limiting flow obtained using the ODE method.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02310672
Contributor : Charles-Edouard Bréhier <>
Submitted on : Thursday, October 10, 2019 - 1:19:58 PM
Last modification on : Monday, October 14, 2019 - 11:33:42 AM

File

BBM-ABF.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02310672, version 1

Citation

Michel Benaïm, Charles-Edouard Bréhier, Pierre Monmarché. Analysis of an Adaptive Biasing Force method based on self-interacting dynamics. 2019. ⟨hal-02310672⟩

Share

Metrics

Record views

14

Files downloads

7