Computationally efficient multiscale estimation of large-scale dynamic systems

Statistical estimation of large-scale dynamic systems governed by stochastic partial differential equations is important in a wide range of scientific applications. However, the realization of computationally efficient algorithms for statistical estimation of such dynamic systems is very difficult. Conventional linear least squares methods are impractical for both computational and storage reasons. A previously-developed multiscale estimation methodology has been successfully applied to a number of large-scale static estimation problems. In this paper we apply the multiscale approach to the more challenging dynamic estimation problems, introducing a recursive procedure that efficiently propagates multiscale models for the estimation errors in a manner analogous to, but more efficient than, the Kalman filter's propagation of the error covariances. We illustrate our research in the context of 1-D and 2-D diffusive processes.