Department of Mathematics, Applied Mathematics and Statistics
Friday, January 31, 2014 (3:00-4:00 pm, Yost 306)
Title: Linear Theory for Filtering Nonlinear Multiscale Systems with Model Error
Speaker: John Harlim (Pennsylvania State University)
Abstract: Fundamental issues in improving state estimation (or filtering) problems are model errors. This problem is attributed to incomplete understanding of the underlying physics and our lack of computational resources to resolve physical processes in various time and length scales. In this talk, we will discuss a linear theory for filtering multiscale dynamical systems with model error. In particular, we will use the notion of "consistency" to show the existence and uniqueness of an optimal filter with a reduced stochastic model. By optimality, we mean both the posterior mean and covariance estimates from the reduced filter matches the true filtered statistical solutions. Subsequently, we will construct an accurate reduced filter in a simple, yet challenging nonlinear setting, where the optimal filter is not available as in practical situation. Finally, we will discuss a stochastic parameterization strategy to account for model errors in filtering high-dimensional nonlinear problems. We will demonstrate our stochastic parameterization method in a numerical example by filtering an 81-dimensional model which exhibits many of the characteristics seen in practical applications using a 9-dimensional reduced model.