相关论文: Accelerated dynamics: Mathematical foundations and…

The objective of this review article is to present recent results on the mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F. Voter in collaboration with D. Perez and M. Sorensen. Using the notion of…

We give a mathematical framework for temperature accelerated dynamics (TAD), an algorithm proposed by M.R. S{\o}rensen and A.F. Voter to efficiently generate metastable stochastic dynamics. Using the notion of quasistationary distributions,…

The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the…

The parallel replica dynamics, originally developed by A.F. Voter, efficiently simulates very long trajectories of metastable Langevin dynamics. We present an analogous algorithm for discrete time Markov processes. Such Markov processes…

This work is concerned with the analysis of a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces. This is a generalization of a method introduced by Aldous, Flannery and Palacios.…

This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…

We present how entropy estimates and logarithmic Sobolev inequalities on the one hand, and the notion of quasi-stationary distribution on the other hand, are useful tools to analyze metastable overdamped Langevin dynamics, in particular to…

In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…

Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast…

Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…

We present a new probabilistic analysis of distributed algorithms. Our approach relies on the theory of quasi-stationary distributions (QSD) recently developped by Champagnat and Villemonais. We give properties on the deadlock time and the…

Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…

We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…

The Milestoning algorithm created by Ron Elber et al. is a method for determining the time scale of processes too complex to be studied using brute force simulation methods. The fundamental objects implemented in the Milestoning algorithm…

Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…

An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…