Mathematical strategies for filtering turbulent dynamical systems

Andrew J. Majda, John Harlim, Boris Gershgorin

Research output: Contribution to journalArticle

Abstract

The modus operandi of modern applied mathematics in developing very recent mathematical strategies for filtering turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines, exactly solvable nonlinear models with physical insight, and novel cheap algorithms with judicious model errors to filter turbulent signals with many degrees of freedom. A large number of new theoretical and computational phenomena such as "catastrophic filter divergence" in finite ensemble filters are reviewed here with the intention to introduce mathematicians, applied mathematicians, and scientists to this remarkable emerging scientific discipline with increasing practical importance.

Original languageEnglish (US)
Pages (from-to)441-486
Number of pages46
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number2
DOIs
StatePublished - Jun 2010

Fingerprint

Dynamical systems
Filtering
Dynamical system
Filter
Solvable Models
Model Error
Synergy
Applied mathematics
Nonlinear Model
Divergence
Ensemble
Degree of freedom
Strategy

Keywords

  • Data assimilation
  • Filtering turbulent systems
  • Kalman filter
  • Model error
  • Stochastic parameter estimation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Mathematical strategies for filtering turbulent dynamical systems. / Majda, Andrew J.; Harlim, John; Gershgorin, Boris.

In: Discrete and Continuous Dynamical Systems, Vol. 27, No. 2, 06.2010, p. 441-486.

Research output: Contribution to journalArticle

Majda, Andrew J. ; Harlim, John ; Gershgorin, Boris. / Mathematical strategies for filtering turbulent dynamical systems. In: Discrete and Continuous Dynamical Systems. 2010 ; Vol. 27, No. 2. pp. 441-486.
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