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 15:0016:00, Building 101, Lecture Room A Gaithersburg Wednesday, July 1, 2009 13:0014:00, Room 4511 Boulder
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 offline 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 supercomputers 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 3years 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. LottNote: Visitors from outside NIST must contact
Robin Bickel; (301) 9753668;
at least 24 hours in advance.
