Real Time Filtering and Parameter Estimation for Dynamical Systems With Many Degrees of Freedom

摘要

Many contemporary problems in science ranging from the spread of hazardous chemical or nuclear plumes to protein folding in molecular dynamics to scale up of small scale effects in nanotechnology, to making accurate predictions of the coupled atmosphere-ocean system involve partial observations of extremely complicated systems with many degrees of freedom. There is a practical need to develop accurate real-time predictions of these extremely complex multi-scale dynamical systems with many degrees of freedom. Novel mathematical issues arise in the attempt to quantify the behavior of such complex multi-scale systems. New mathematical issues arise in the practical application of these filtering strategies to complex spatially extended systems in order to do rapid prediction including assessments of uncertainty from model error and parameter estimation and this is the focus for the present seed proposal.