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Journal Articles The Annals of Applied Probability Year : 2022

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

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Abstract

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 5-dimensional reaction coordinates demonstrate that the method is indeed able to capture correlations between them.
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Dates and versions

hal-02314426 , version 1 (13-12-2019)
hal-02314426 , version 2 (20-07-2020)
hal-02314426 , version 3 (19-11-2021)

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Virginie Ehrlacher, Tony Lelièvre, Pierre Monmarché. Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias. The Annals of Applied Probability, 2022, 32 (5), ⟨10.1214/21-AAP1775⟩. ⟨hal-02314426v3⟩
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