A list-based algorithm for evaluation of large deviation functions

Tchernookov, Martin; Dinner, Aaron R.

doi:10.1088/1742-5468/2010/02/p02006

Cited by 11 publications

(18 citation statements)

References 17 publications

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“…Our model and code proves to be a very efficient tool to study not only the (2 + 1) dimensional KPZ and ASEP models but, more generally it can be used in the research of fundamental nonequilibrium thermodynamical quantities like the large deviation function or entropy production [49,50]. It is also straightforward to extend it to study more complex system exhibiting pattern formation [51,52], the effect of quenched disorder [54], the time-dependent structure factor [53] or to higher dimensions [29].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Kelling

Ódor

2011

Phys. Rev. E

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The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large scale simulations via binary lattice gases and bit coded algorithms. We confirm scaling behavior belonging to the two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: β = 0.2415(15) on 2 17 × 2 17 systems, ruling out β = 1/4 suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite size scaling and a growth exponent α = 0.393(4) is found. Correction-to-scaling exponents are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions, cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Kelling

Ódor

2011

Phys. Rev. E

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“…This is the strategy proposed in diffusion Monte Carlo (DMC), and has been adopted for the study of nonequilibrium classical stochastic dynamics by algorithms known as forward flux sampling, and the so-called cloning algorithm. 12,16,55 In both methods, an ensemble of initial conditions is generated using some prior distribution. Each initial condition, referred to here as a walker, is propagated for some short time, creating an ensemble of short trajectories.…”

Section: B Diffusion Monte Carlomentioning

confidence: 99%

Importance sampling large deviations in nonequilibrium steady states. I

Ray

Chan

Limmer

2018

The Journal of Chemical Physics

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Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

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“…The limitations and * esteban guevarah@hotmail.com; nemoto@lpt.ens.fr; vivien.lecomte@univ-grenoble-alpes.fr associated improvements of the population dynamics algorithm have been studied in Refs. [9][10][11][12]. In this paper, following a different approach, we propose an original and simple method that takes into account the exact scalings of the finite-t and finite-N c corrections in order to provide significantly better LDF estimators.…”

Section: Introductionmentioning

confidence: 99%

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time

2017

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Rare trajectories of stochastic systems are important to understand -because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor the rare trajectories of interest. Such algorithms are plagued by finite simulation time-and finite population size-effects that can render their use delicate. In this paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators which -as shown on the contact process -provides a significant improvement of the large deviation functions estimators compared to the the standard one.

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A list-based algorithm for evaluation of large deviation functions

Cited by 11 publications

References 17 publications

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Importance sampling large deviations in nonequilibrium steady states. I

Finite-time and finite-size scalings in the evaluation of large-deviation functions: Numerical approach in continuous time

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