| Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 529 - 564 | |
| DOI | https://doi.org/10.1051/m2an/2022010 | |
| Published online | 28 February 2022 | |
The adaptive biasing force algorithm with non-conservative forces and related topics
1
Université Paris-Est, CERMICS (ENPC), Inria, 77455 Marne-la-Vallée, France
2
Sorbonne Université, LJLL, 4 place Jussieu, 75005 Paris, France
3
Sorbonne Université, LCT, 4 place Jussieu, 75005 Paris, France
* Corresponding author: lise.maurin@sorbonne-universite.fr
Received:
4
March
2021
Accepted:
21
January
2022
We propose a study of the Adaptive Biasing Force method’s robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding the existence of a stationary state for both the Adaptive Biasing Force and Projected Adapted Biasing Force algorithms, relying on generic bounds on the invariant probability measures of homogeneous diffusions. Using classical entropy techniques, we prove the exponential convergence of both biasing force and law as time goes to infinity, for both the Adaptive Biasing Force and the Projected Adaptive Biasing Force methods.
Mathematics Subject Classification: 35B40 / 60J60
Key words: Adaptive Bisaing Force / nonlinear Fokker-Planck equation / long-time behaviour / free energy / entropy techniques
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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