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Full-Text Articles in Physical Sciences and Mathematics
Goal-Oriented Sensitivity Analysis For Lattice Kinetic Monte Carlo Simulations, Georgios Arampatzis, Markos Katsoulakis
Goal-Oriented Sensitivity Analysis For Lattice Kinetic Monte Carlo Simulations, Georgios Arampatzis, Markos Katsoulakis
Markos Katsoulakis
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the …
Parallelization, Processor Communication And Error Analysis In Lattice Kinetic Monte Carlo, Giorgos Arampatzis, Markos Katsoulakis, Petr Plechac
Parallelization, Processor Communication And Error Analysis In Lattice Kinetic Monte Carlo, Giorgos Arampatzis, Markos Katsoulakis, Petr Plechac
Markos Katsoulakis
In this paper we study from a numerical analysis perspective the fractional step kinetic Monte Carlo (FS-KMC) algorithms proposed in [G. Arampatzis, M. A. Katsoulakis, P. Plechac, M. Taufer, and L. Xu, J. Comput. Phys., 231 (2012), pp. 7795--7814] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are fractional step algorithms with a time-stepping window $\Delta t$, and as such they are inherently partially asynchronous since there is no processor communication during the period $\Delta t$. In this contribution we primarily focus on the error analysis of FS-KMC algorithms as approximations of conventional, serial KMC. …
Measuring The Irreversibility Of Numerical Schemes For Reversible Stochastic Differential Equations, Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet
Measuring The Irreversibility Of Numerical Schemes For Reversible Stochastic Differential Equations, Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet
Markos Katsoulakis
For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility of discrete-time approximation processes. In this paper we provide such quantitative estimates by using the concept of entropy production rate, inspired by ideas from non-equilibrium statistical mechanics. The entropy production rate for a stochastic …
Spatial Multi-Level Interacting Particle Simulations And Information Theory-Based Error Quantification, Evangelia Kalligiannaki, Markos Katsoulakis, Petr Plechac
Spatial Multi-Level Interacting Particle Simulations And Information Theory-Based Error Quantification, Evangelia Kalligiannaki, Markos Katsoulakis, Petr Plechac
Markos Katsoulakis
We propose a hierarchy of two-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and developing local reconstruction strategies from coarse-grained dynamics. Furthermore, a natural extension to a multilevel kinetic coarse-grained Monte Carlo is presented. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed algorithm overcomes known shortcomings of coarse-graining of particle systems with complex …