Computationally Efficient Multiscale Estimation of Large-Scale Dynamic Systems

Statist ical es t imat ion of large-scale dynamic sys tems governed by stochastic partial differential equations i s impor tant in a wide range of scientific applications. However, t he realization of computationally e f i c i en t algor i thms f o r statistical es t imat ion of such dynamic syst e m s i s ve ry d i f icu l t . Convent ional linear least squares methods are impractical f o r both computational and storage reasons. A recently-developed multiscale es t imat ion methodology has been successfully applied t o a number of largescale static es t imat ion problems. In th is paper we app l y the multiscale approach t o the more challenging dynamic es t imat ion problems, introducing a recursive procedure tha t e f i c i en t l y propagates multiscale models for t he es t imat ion errors in a m a n n e r analogous to , but more e f i c i e n t t han , t he K a l m a n filter’s propagation of the error covariances. W e will illustrate our research in the contex t of 1-D and 2 0 diffusive processes.