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Comparison of
continuous and discrete-time data-based modeling for
hypoelliptic systems
Fei Lu, Kevin K. Lin and Alexandre J. Chorin |
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Vol. 11 (2016), No. 2, 187–216
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Abstract |
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We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations, which are then discretized for numerical solution. The second is discrete in time, where one directly infers a discrete-time model in the form of a nonlinear autoregression moving average model. The comparison is performed in a special case where the observations are known to have been obtained from a hypoelliptic stochastic differential equation. We show that the discrete-time approach has better predictive skills, especially when the data are relatively sparse in time. We discuss open questions as well as the broader significance of the results. |
Keywords
hypoellipticity, stochastic parametrization, Kramers
oscillator, statistical inference, discrete partial data,
NARMA
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Mathematical Subject Classification 2010
Primary: 62M09, 65C60
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Milestones
Received: 31 May 2016
Revised: 6 December 2016
Accepted: 6 December 2016
Published: 20 December 2016
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Authors |
| Fei Lu | |
| Department of Mathematics University of California, Berkeley Evans Hall Berkeley, CA 94720-3840 United States |
Lawrence Berkeley National
Laboratory Berkeley, CA 94720 United States |
| Kevin K. Lin | |
| Department of Mathematics University of Arizona 617 North Santa Rita Avenue Tucson, AZ 85721-0089 United States |
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| Alexandre J. Chorin | |
| Department of Mathematics University of California, Berkeley Evans Hall Berkeley, CA 94720-3840 United States |
Lawrence Berkeley National
Laboratory Berkeley, CA 94720 United States |
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