Parameterization of stochastic multiscale triads

We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction metho...

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Bibliographic Details
Published in:Nonlinear processes in geophysics 2016-11, Vol.23 (6), p.435-445
Main Authors: Wouters, Jeroen, Dolaptchiev, Stamen Iankov, Lucarini, Valerio, Achatz, Ulrich
Format: Article
Language:English
Subjects:
Dynamical systems
Geophysics
Markov analysis
Parameter identification
Stochastic models
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Summary:We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system; we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost.
ISSN:1607-7946
1023-5809
1607-7946
DOI:10.5194/npg-23-435-2016