Lessons in uncertainty quantification for turbulent dynamical systems

Andrew J. Majda, Michal Branicki

Research output: Contribution to journalReview articlepeer-review


The modus operandi of modern applied mathematics in developing very recent mathematical strategies for uncertainty quantification in partially observed high-dimensional turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines with a suite of physically relevant and progressively more complex test models which are mathematically tractable while possessing such important features as the two-way coupling between the resolved dynamics and the turbulent uxes, intermittency and positive Lyapunov exponents, eddy diffusivity parameterization and turbulent spectra. A large number of new theoretical and computational phenomena which arise in the emerging statistical-stochastic framework for quantifying and mitigating model error in imperfect predictions, such as the existence of information barriers to model improvement, are developed and reviewed here with the intention to introduce mathematicians, applied mathematicians, and scientists to these remarkable emerging topics with increasing practical importance.

Original languageEnglish (US)
Pages (from-to)3133-3221
Number of pages89
JournalDiscrete and Continuous Dynamical Systems
Issue number9
StatePublished - Sep 2012


  • Fiuctuation-dissipation theorems
  • Information barriers
  • Information theory
  • Model error
  • Prediction
  • Stochastic PDE's
  • Turbulent systems
  • Uncertainty quantification

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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