Vol. 11, No. 2, 2016

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems

Fei Lu, Kevin K. Lin and Alexandre J. Chorin

Vol. 11 (2016), No. 2, 187–216
Abstract

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
Mathematical Subject Classification 2010
Primary: 62M09, 65C60
Milestones
Received: 31 May 2016
Revised: 6 December 2016
Accepted: 6 December 2016
Published: 20 December 2016
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
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