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Extracting macroscopic stochastic dynamics: Model problems

Huisinga, Wilhelm and Schütte, Christof and Stuart, Andrew M. (2003) Extracting macroscopic stochastic dynamics: Model problems. Communications on Pure and Applied Mathematics, 56 (2). pp. 234-269. ISSN 0010-3640. doi:10.1002/cpa.10057.

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The purpose of this work is to shed light on an algorithm designed to extract effective macroscopic models from detailed microscopic simulations. The particular algorithm we study is a recently developed transfer operator approach due to Schütte et al. [20]. The investigations involve the formulation, and subsequent numerical study, of a class of model problems. The model problems are ordinary differential equations constructed to have the property that, when projected onto a low-dimensional subspace, the dynamics is approximately that of a stochastic differential equation exhibiting a finite-state-space Markov chain structure. The numerical studies show that the transfer operator approach can accurately extract finite-state Markov chain behavior embedded within high-dimensional ordinary differential equations. In so doing the studies lend considerable weight to existing applications of the algorithm to the complex systems arising in applications such as molecular dynamics. The algorithm is predicated on the assumption of Markovian input data; further numerical studies probe the role of memory effects. Although preliminary, these studies of memory indicate interesting avenues for further development of the transfer operator methodology.

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Additional Information:© 2002 Wiley Periodicals, Inc. Issue online: 26 November 2002; Version of record online: 26 November 2002; Manuscript Received: January 2002. We are grateful to A. J. Majda for encouraging the collaboration that led to this work. We are grateful to A. J. Majda, E. Vanden Eijnden, and P. F. Tupper for illuminating and insightful discussions. W. Huisinga was supported by "Deutsche Forschungsgesellschaft" within SPP 1095: "Analysis, Modeling and Simulation of Multiscale Problems." A. M. Stuart is supported by the EPSRC.
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Deutsche Forschungsgemeinschaft (DFG)SPP 1095
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
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Andrew StuartJ56
Issue or Number:2
Record Number:CaltechAUTHORS:20170609-144239769
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Official Citation:Huisinga, W., Schütte, C. and Stuart, A. M. (2003), Extracting macroscopic stochastic dynamics: Model problems. Comm. Pure Appl. Math., 56: 234–269. doi:10.1002/cpa.10057
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78069
Deposited By: Tony Diaz
Deposited On:09 Jun 2017 22:22
Last Modified:15 Nov 2021 17:36

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