Blended particle filters for large-dimensional chaotic dynamical systems

Andrew J. Majda, Di Qi, Themistoklis P. Sapsis

Research output: Contribution to journalArticlepeer-review


A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimen-sional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below.

Original languageEnglish (US)
Pages (from-to)7511-7516
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number21
StatePublished - May 27 2014


  • Curse of dimensionality
  • Hybrid methods

ASJC Scopus subject areas

  • General


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