Title: Model Order Reduction and Optimal Control applied to Geophysical Fluid Dynamics Speaker: Xiao Chen, Florida State University Date/Time: Monday, March 7, 2011 Location: CSRI Building/Room 90 (Sandia NM) Brief Abstract: Applications of 4-D variational data assimilation (4-D Var) arise in many fields of geosciences, perhaps most importantly in numerical weather forecasting and computational hydrology. The objective of 4-D Var is to obtain the minimum of a cost functional estimating the discrepancy between the model solutions and distributed observations. Derivation of the optimality system involves an adjoint model, which provides the gradient of a cost functional with respect to the initial conditions that are used as control variables in the optimization. Standard spatial discretization schemes for a dynamic system usually lead to large-scale, high-dimensional, and in general, nonlinear systems of ordinary differential equations. Due to limited computational and storage capabilities, a control reduction methodology based on Proper Orthogonal Decomposition (POD), referred to as POD 4-D Var, has been widely used for nonlinear systems with tractable computations. However, the appropriate criteria for updating a POD reduced order modeling (ROM) are not yet known in the application to optimal control. This is due to the limited validity of the POD ROM for inverse problems. Therefore, the classical Trust-Region (TR) approach combined with POD (TRPOD) was proposed as a way to overcome the above difficulties. In order to reduce the POD basis size, another novel method was proposed to incorporate information from the 4-D Var system into the ROM procedure by implementing a dual weighted POD method. We conclude that POD 4-D Var certainly warrants further studies, with promising potential of its extension to operational 3-D numerical weather prediction models and application to uncertainty quantification. Directions of future research are finally outlined.CSRI POC: Jim Stewart, 505-844-8630 |