Parallel tempering

Résumé

Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures may become "stuck" in a metastable state. It does this by using the fact that the high temperature simulation may visit states typical of both stable and metastable low temperature states. More specifically, parallel tempering (also known as replica exchange MCMC sampling), is a simulation method aimed at improving the dynamic properties of Monte Carlo method simulations of physical systems, and of Markov chain Monte Carlo (MCMC) sampling methods more generally. The replica exchange method was originally devised by Robert Swendsen and J. S. Wang, then extended by Charles J. Geyer, and later developed further by Giorgio Parisi, Koji Hukushima and Koji Nemoto, and o

Source officielle

https://en.wikipedia.org/wiki/Parallel_tempering

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Repetition of the basic concepts of quantum mechanics and main numerical algorithms used for practical implementions. Basic principles of electronic structure methods:Hartree-Fock, many body perturbation theory, configuration interaction, coupled-cluster theory, density functional theory.

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Hydrocontest – Computational Fluid Dynamics of Hydrofoils

Fabio Stradelli

HYDROcontest is a challenge open to students from 13 universities from all over the world. The aim of the competition is to design the motorboat that best fulfills the tradeoff between high speed and low energy consumption. In order to optimize the shape of the hydrofoils sustaining the boat, suitable Computational Fluid Dynamics models and parallel simulations were employed. The variational multiscale (VMS) model proposed by Bazilevs et al. (2009) was linearized by means of a Newton method, discretized in time through a fully-implicit scheme, transformed into a dimensionless form and implemented in C++, using the Finite Elements library LifeV.

2014

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MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems

Juan Pablo Madrigal Cianci, Fabio Nobile

In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood as the limit case of the continuous-time Parallel Tempering algorithm, where the (random) time between swaps of states between two parallel chains goes to zero. Thus, swapping states between chains occurs continuously. In the current work, we extend this idea to the context of time-discrete Markov chains and present two Markov chain Monte Carlo algorithms that follow the same paradigm as the continuous-time infinite swapping procedure. We analyze the convergence properties of such discrete-time algorithms in terms of their spectral gap, and implement them to sample from different target distributions. Numerical results show that the proposed methods significantly improve sampling efficiency over more traditional sampling algorithms such as Random Walk Metropolis and (traditional) Parallel Tempering.

MATHICSE2020

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MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems

Juan Pablo Madrigal Cianci, Fabio Nobile

Chargement