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.