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Kernel Analog Forecasting: Multiscale Test Problems

Burov, Dmitry and Giannakis, Dimitrios and Manohar, Krithika and Stuart, Andrew (2021) Kernel Analog Forecasting: Multiscale Test Problems. Multiscale Modeling and Simulation, 19 (2). pp. 1011-1040. ISSN 1540-3459. doi:10.1137/20M1338289. https://resolver.caltech.edu/CaltechAUTHORS:20201109-140959408

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Abstract

Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions made and the manner in which they should be interpreted depend crucially on the extent to which the variables chosen for prediction are Markovian or approximately Markovian. Multiscale systems provide a framework in which this issue can be analyzed. In this work kernel analog forecasting methods are studied from the perspective of data generated by multiscale dynamical systems. The problems chosen exhibit a variety of different Markovian closures, using both averaging and homogenization; furthermore, settings where scale separation is not present and the predicted variables are non-Markovian are also considered. The studies provide guidance for the interpretation of data-driven prediction methods when used in practice.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1137/20M1338289DOIArticle
https://arxiv.org/abs/2005.06623arXivDiscussion Paper
ORCID:
AuthorORCID
Manohar, Krithika0000-0002-1582-6767
Stuart, Andrew0000-0001-9091-7266
Additional Information:© 2021, Society for Industrial and Applied Mathematics. Received by the editors May 18, 2020; accepted for publication (in revised form) February 2, 2021; published electronically June 16, 2021. Funding: The first and fourth authors were supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by Earthrise Alliance, Mountain Philanthropies, the Paul G. Allen Family Foundation, and the National Science Foundation (NSF) (award AGS1835860). The second author is supported by NSF (awards 1842538 and DMS-1854383) and ONR (awards N00014-16-1-2649 and N00014-19-1-242). The third author is supported by the NSF Mathematical Sciences Postdoctoral Research Fellowship (award 1803663). The fourth author is also supported by NSF (award DMS-1818977) and by the Office of Naval Research (award N00014-17-1-2079). DG is grateful to the Department of Computing and Mathematical Sciences at the California Institute of Technology for hospitality and for providing a stimulating environment during a sabbatical where part of this work was completed.
Funders:
Funding AgencyGrant Number
Schmidt Futures ProgramUNSPECIFIED
Earthrise AllianceUNSPECIFIED
Mountain PhilanthropiesUNSPECIFIED
Paul G. Allen Family FoundationUNSPECIFIED
NSFAGS-1835860
NSFAGS-1842538
NSFDMS-1854383
Office of Naval Research (ONR)N00014-16-1-2649
Office of Naval Research (ONR)N00014-19-1-2421
NSF Mathematical Sciences FellowshipDMS-1803663
NSFDMS-1818977
Office of Naval Research (ONR)N00014-17-1-2079
Subject Keywords:data-driven prediction, multiscale systems, kernel methods, analog forecasting, averaging, homogenization
Issue or Number:2
Classification Code:AMS subject classifications: 37M10, 34E13, 58J65
DOI:10.1137/20M1338289
Record Number:CaltechAUTHORS:20201109-140959408
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201109-140959408
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106559
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:09 Nov 2020 22:53
Last Modified:20 Aug 2021 17:14

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