Mathematical Strategies for Filtering Turbulent Signals in Complex Systems

by Andrew J. Majda
Morse Professor of Arts and Sciences
Department of Mathematics and Climate, Atmosphere, Ocean Science (CAOS)
Courant Institute of Mathematical Sciences

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 as well as the statistical accuracy of various strategies in this context. This lecture is an introduction to the mathematical theories and ideas which are currently being developed at CIMS by John Harlim and the lecturer to address these issues. These ideas blend classical stability analysis for PDE’s and their finite difference approximations, suitable versions of Kalman filtering, and stochastic models from turbulence theory to deal with the large model errors in realistic systems. Emerging applications to fully turbulent and chaotic nonlinear systems will also be discussed.