Combining stochastic and deterministic approaches within high efficiency molecular simulations

Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle's velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians, the asymptotic expansions in powers of the discretization parameter corresponding to timestep, which are conserved by symplectic integrators to higher accuracy than true Hamiltonians. We present the implementation of this method into the highly efficient MD code GROMACS and demonstrate its performance and accuracy on computationally expensive systems like proteins in comparison with the molecular dynamics techniques already available in GROMACS. We take advantage of the state-of-the-art algorithms adopted in the code, leading to an optimal implementation of the method. Our implementation introduces virtually no overhead and can accurately recreate complex biological processes, including rare event dynamics, saving much computational time compared with the conventional simulation methods

Effective algorithms for simulation of Discrete-Event systems

Import 22/07/2015Tato diplomová práce se zabývá simulací DE systémů, tedy takových systémů, k jejichž změnám dochází v diskrétních časových okamžicích. Simulace je založena na metodě Monte Carlo a její efektivita je zajištěna použitím metod redukce rozptylu a pokročilými způsoby implementace. Použitými metodami redukce rozptylu jsou metoda antitetických náhodných veličin, metoda řídících veličin, podmíněná metoda Monte Carlo a metoda importance sampling, je kladen důraz na kvantifikaci řídkých jevů. Práce se dále zabývá analýzou citlivosti DE systémů pomocí metody centrálních diferencí a metody score function. Všechny zmíněné metody byly implementovány v jazyce Matlab a poté paralelizovány na GPU pomocí technologie CUDA. Simulační metody byly dále aplikovány na problémy z oblasti spolehlivosti systémů.This master thesis focuses on DE systems simulation, the changes of these systems occur at discrere points of time. The simulation is based on the Monte Carlo method and its effectivity is ensured by using variance reduction techniques and advanced methods of implementation. The variance reduction methods include antithetic random variables, control variables, conditional Monte Carlo and importance sampling, the emphasis is on rare event probabilities estimation. The thesis also deals with sensitivity analysis of DE systems using central differences and the score function method. All of the methods were implemented in Matlab and GPU parallelized using CUDA technology. The simulation methods were also applied to problems of system reliability.470 - Katedra aplikované matematikyvýborn

Split Sampling: Expectations, Normalisation and Rare Events

In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling