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

Virginie Ehrlacher, Tony Lelièvre, Pierre Monmarché

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Geometric sums, size biasing and zero biasing

The geometric sum plays a significant role in risk theory and reliability theory \cite{Kala97} and a prototypical example of the geometric sum is Rényi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised geometric sums converges to the exponential distribution. There is extensive study of the accuracy of exponential distribution approximation to the geometric sum \cite{Sugakova95,Kala97,PekozRollin11} but there is little study on its natural counterpart of gamma distribution approximation to negative binomial sums. In this note, we show that a nonnegative random variable follo…

2021-10-16math.PR

Variance Reduction Result for a Projected Adaptive Biasing Force Method

This paper is committed to investigate an extension of the classical adaptive biasing force method, which is used to compute the free energy related to the Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this technique is that the approximated gradient of the free energy, called biasing force, is not a gradient. The commitment to this field is to project the estimated biasing force on a gradient using the Helmholtz decomposition. The variance of the biasing force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method. We …

2017-11-07math.PR

Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process

We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to approximate this conditional expectation, providing a discretization scheme for this equation.

2010-01-16math.PR

通过独立增量进行偏置：高斯近似与泊松混合分布的接近性

Biasing with an independent increment: Gaussian approximations and proximity of Poisson mixtures

Heriot–Watt University（赫瑞-瓦特大学）

本文通过独立增量偏置方法，建立了泊松混合分布的高斯近似结果及中心极限定理，适用于迪克曼型极限定理等应用。

2025-12-10math.PR

从Wasserstein优化视角看适应性偏置势方案的收敛速率

Convergence rates for an Adaptive Biasing Potential scheme from a Wasserstein optimization perspective

CERMICS, ENPC, Institut Polytechnique de Paris, and Inria（CERMICS，巴黎高等工程学校，巴黎理工学院，法国国家信息与自动化研究所）；École Polytechnique（巴黎综合理工学院）；Sorbonne Université, Laboratoire Jacques-Louis Lions & Laboratoire de Chimie théorique, LJLL & LCT（索邦大学，雅克-路易·利翁斯实验室与理论化学实验室）；Institut Universitaire de France（法兰西学院）

本文从Wasserstein优化视角出发，首次对适应性偏置势方案的动能Langevin扩散进行了指数收敛性分析，揭示了其在理想化设定下的理论收敛速率。

2026-01-28math.PR

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

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…

2019-10-10math.PR

更多相关论文收起更多论文

Refined properties for the Mellin transform, with applications to convergence of families obtained by biasing or by the stationary excess operator

We first provide some properties of the Mellin transform of nonnegative random variables, such that monotonicity, injectivity and effect of size biasing. Convergence of Mellin transforms is also entirely formalized through convergence in distribution and uniform integrability. As an application, we study a problem raised by Harkness and Shantaram (1969) who obtained, under sufficient conditions, a limit theorem for sequences of nonnegative random variables build with the iterated stationary excess operator. We reformulate this problem through the concept of multiply monotone functions and thro…

2016-06-12math.PR

Convergence analysis of Adaptive Biasing Potential methods for diffusion processes

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently sample the invariant distribution of the diffusion process, thanks to the approximation of the associated free energy function (relative to a reaction coordinate). The bias which is introduced in the dynamics is computed adaptively; it depends on the past of the trajectory of the process through some time-averages. We give a detailed and general construction o…

2018-05-09math.PR