ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Mathematical Strategies for Filtering Turbulent Systems: Sparse Observations, Model Errors, and Stochastic Parameter Estimation

John Harlim
Courant Institute of Mathematical Sciences, New York University, New York, NY

Wednesday, July 1, 2009 15:00-16:00,
Building 101, Lecture Room A
Wednesday, July 1, 2009 13:00-14:00,
Room 4511

Abstract: An important emerging scientific issue in many practical problems ranging from climate and weather prediction to biological science involves the real time filtering and prediction through partial observations of noisy turbulent signals for complex dynamical systems with many degrees of freedom. In this talk, I will present a novel reduced filtering strategy by blending ideas from classical stability analysis for PDE's, Kalman filter, and stochastic models from turbulence theory. Our new strategy is not only computationally attractive but also clarifies many theoretical issues and provides off-line criteria for filtering in many turbulent regimes. The second aspect of the talk deals with model errors in modeling turbulent signals. These errors are often unavoidable due to our inability to justify the physical processes and/or to even numerically resolve some physical processes with current super-computers even if they are well understood. I will describe a radical strategy which produces nontrivial filtering skill with judicious model errors, avoiding the ``catastrophic filter divergence" exhibited by the perfect model in a fully turbulent regime when observations are sparse. Finally, I will present the ``Nonlinear Extended Kalman Filter" (NEKF) algorithm that systematically corrects both multiplicative and additive bias in an imperfect model. There are both significantly improved filtering and predictive skill through the NEKF stochastic parameter estimation algorithms provided that these are guided by mathematical theory.

Speaker Bio: John Harlim received his Ph.D. in applied mathematics from the University of Maryland, College Park, in 2006. Following his Ph.D., he worked for 3-years as a postdoctoral fellow at the Courant Institute, New York University, and he will become an assistant professor of mathematics at the North Carolina State University starting this fall. His main scientific interest is to develop strategies and mathematical criteria for filtering sparsely observed turbulent complex systems based on the classical Kalman filter theory, the Von Neumann's stability criteria for numerical PDE's, and the stochastic modeling for turbulent signals.

Presentation Slides: PDF

Contact: A. Lott

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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