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Type: Conference paper
Title: Projective integration of expensive multiscale stochastic simulation
Other Titles: Projective integration of expensive stochastic processes
Author: Chen, X.
Roberts, A.
Kevrekidis, I.
Citation: ANZIAM Journal, 2010; 52: C661-C677
Publisher: Cambridge University Press
Publisher Place: United Kingdom
Issue Date: 2011
ISSN: 1446-1811
Conference Name: Biennial Computational Techniques and Applications Conference (15th : 2010 : Sydney, N.S.W.)
Statement of
Xiaopeng Chen, Anthony J. Roberts and Ioannis Kevrekidis
Abstract: Consider the case when a microscale simulator is too expensive for long time simulations necessary to determine macroscale dynamics. Projective integration uses bursts of the microscale simulator, using microscale time steps, and computes an approximation to the system over a macroscale time step by extrapolation. Projective integration has the potential to be an effective method to compute the long time dynamic behaviour of multiscale systems. However, many multiscale systems are influenced by noise. Thus it is important to consider the projective integration of such systems. By the maximum likelihood estimation, we estimate a linear stochastic differential equation from short bursts of data. The analytic solution of the linear stochastic differential equation then estimates the solution over a macroscale time step. We explore how the noise affects the projective integration in different methods. Monte Carlo simulation suggests design parameters offering stability and accuracy for the algorithms. The algorithms developed here may be applied to compute the long time dynamic behaviour of multiscale systems with noise.
Keywords: stochastic differential equations, stochastic process, projective integration, maximum likelihood estimation
Description: The 15th Biennial Computational Techniques and Applications Conference, held at the University of New South Wales, 28 November - 1 December 2010
Rights: © Austral. Mathematical Soc. 2011.
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