Data-Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns

Dimitrios Glannakis, Andrew J. Majda

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter reviews two examples of applied mathematics techniques for data analysis in dynamical systems. The two examples are: (1) Methods for quantifying predictability and model error based on data clustering and information theory and (2) nonlinear Laplacian spectral analysis (NLSA) algorithms for extracting spatiotemporal patterns from high-dimensional data. The chapter highlights these techniques with applications to climate atmosphere ocean science (CAOS), in particular, predictability assessment and Markov modeling of circulation regimes in a simple ocean model and extraction of modes of organized convection in the tropics from infrared brightness temperature satellite data. A common theme in these methods has been the coarse-grained geometry of the data. The machinery of discrete exterior calculus and spectral graph theory was combined with delay-coordinate mappings of dynamical systems to extract spatiotemporal modes of variability which are describable in terms of low-dimensional sets of diffusion eigenfunctions.

Original languageEnglish (US)
Title of host publicationMathematical and Computational Modeling
Subtitle of host publicationWith Applications in Natural and Social Sciences, Engineering, and the Arts
PublisherWiley
Pages137-191
Number of pages55
ISBN (Electronic)9781118853986
ISBN (Print)9781118853887
DOIs
StatePublished - May 8 2015

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Keywords

  • Climate atmosphere ocean science
  • Data clustering
  • Information theory
  • Markov modeling
  • Nonlinear Laplacian spectral analysis algorithms
  • Spatiotemporal patterns

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Chemistry(all)
  • Computer Science(all)

Cite this

Glannakis, D., & Majda, A. J. (2015). Data-Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns. In Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts (pp. 137-191). Wiley. https://doi.org/10.1002/9781118853887.ch7