Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems

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

doi:10.2140/camcos.2016.11.187

Title: Comparison of continuous and discrete-time data-based modeling for hypoelliptic systems

Journal Article · Tue Dec 20 00:00:00 EST 2016 · Communications in Applied Mathematics and Computational Science

DOI:https://doi.org/10.2140/camcos.2016.11.187· OSTI ID:1508052

Lu, Fei ^[1]; Lin, Kevin K. ^[2]; Chorin, Alexandre J. ^[1]

Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of Arizona, Tucson, AZ (United States)

In this work, 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. Finally , we discuss open questions as well as the broader significance of the results.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1508052

Journal Information:: Communications in Applied Mathematics and Computational Science, Vol. 11, Issue 2; ISSN 1559-3940

Publisher:: Mathematical Sciences PublishersCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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Data-Driven Model Reduction for Stochastic Burgers Equations Lu, Fei Entropy, Vol. 22, Issue 12 https://doi.org/10.3390/e22121360	journal	November 2020

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