Accurate Data Assimilation With Sparse Measurements
Daniel Rey, University of California, San Diego
State and parameter estimation of dynamic systems is a fundamental problem involving the validation of mathematical models with measured data and quantitative prediction. This process of transferring information from observations to models of complex systems may meet impediments when the number of observations at any observation time is insufficient. This is especially so when chaotic behavior is expressed, as sensitivity to initial conditions introduces instability into the search procedures, rendering optimization of unknown states and parameters intractable. We show how to use time-delay embedding, familiar from nonlinear dynamics, to provide the information necessary to obtain the accurate state and parameter estimates required to predict future behavior. This method may be critical in allowing the understanding of prediction in complex systems as varied as nervous systems and weather prediction where insufficient measurements are typical.
Abstract Author(s): Daniel Rey, Michael Eldridge, Uriel Morone, Mark Kostuk, Henry D.I. Abarbanel, Jan Schumann-Bischoff, Ulrich Parlitz