Related papers: The Adaptive Biasing Force algorithm with non-cons…
In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. The associated stochastic process satisfies a non linear stochastic differential equation. Using…
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…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
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…
This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…
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…
We prove the consistency of an adaptive importance sampling strategy based on biasing the potential energy function $V$ of a diffusion process $dX_t^0=-\nabla V(X_t^0)dt+dW_t$; for the sake of simplicity, periodic boundary conditions are…
We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…
This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…
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…
Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular simulations. Although their efficiency has been empirically…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
We present convergence results for an adaptive algorithm to compute free energies, namely the adaptive biasing force (ABF) method. The free energy is the effective potential associated to a so-called reaction coordinate (RC). Computing free…
For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…