Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

Evangelia Kalligiannaki; Markos A. Katsoulakis; Petr Plecháč; Dionisios G. Vlachos

doi:10.1016/j.jcp.2011.12.011

Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

Evangelia Kalligiannaki^*, Markos A. Katsoulakis, Petr Plecháč, Dionisios G. Vlachos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.

Original language	English (US)
Pages (from-to)	2599-2620
Number of pages	22
Journal	Journal of Computational Physics
Volume	231
Issue number	6
DOIs	https://doi.org/10.1016/j.jcp.2011.12.011
State	Published - Mar 20 2012
Externally published	Yes

Bibliographical note

Funding Information:
The research was supported by the National Science Foundation, E.K. and P.P. under the Grant NSF-CMMI-0835582, M.A.K. under the Grant NSF-CMMI-0835673 and DMS-715125 and D.G.V. under the Grant NSF-CMMI-0835548.

Keywords

Coarse graining
Lattice systems
Markov chain Monte Carlo
Pattern formation
Phase transitions

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2011.12.011

Cite this

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abstract = "In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.",

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author = "Evangelia Kalligiannaki and Katsoulakis, {Markos A.} and Petr Plech{\'a}{\v c} and Vlachos, {Dionisios G.}",

note = "Funding Information: The research was supported by the National Science Foundation, E.K. and P.P. under the Grant NSF-CMMI-0835582, M.A.K. under the Grant NSF-CMMI-0835673 and DMS-715125 and D.G.V. under the Grant NSF-CMMI-0835548. ",

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AU - Katsoulakis, Markos A.

AU - Plecháč, Petr

AU - Vlachos, Dionisios G.

N1 - Funding Information: The research was supported by the National Science Foundation, E.K. and P.P. under the Grant NSF-CMMI-0835582, M.A.K. under the Grant NSF-CMMI-0835673 and DMS-715125 and D.G.V. under the Grant NSF-CMMI-0835548.

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AB - In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.

KW - Coarse graining

KW - Lattice systems

KW - Markov chain Monte Carlo

KW - Pattern formation

KW - Phase transitions

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Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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