Navaratnam Sri Namachchivaya, Department of Applied Mathematics, University of Waterloo
"Multi-scale Dynamics and Information"
An emerging challenge for inference and prediction of large-scale complex systems is to efficiently analyze and assimilate the ever-increasing high dimensional data produced by the vast number of engineered and natural systems. I shall present results that deal with dimensional reduction and filtering techniques for nonlinear dynamical system with multi-scales. When the rates of change of different variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal. In particular, we study how scaling interacts with filtering via homogenization. We present the main ideas and result of the theory and then describe a particle filter that blends the homogenization result with multi-scale numerical integration. The results are applied to real time filtering of chaotic signals from atmospheric models involving many degrees of freedom.
MC 5501