2021/02/19 by Tony Lelièvre, Lelièvre, Tony, Lise Maurin +3
Decision Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design
paper · doi:10.48550/arxiv.2102.09957
openalex publication_date 2021/02/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
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.