Kernel analog forecasting: Multiscale test problems

Dmitry Burov, Dimitrios Giannakis, Krithika Manohar, Andrew Stuart

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1011-1040
Number of pages30
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - 2021


  • Analog forecasting
  • Averaging
  • Data-driven prediction
  • Homogenization
  • Kernel methods
  • Multiscale systems

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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