The Institut de Mathématiques de Bordeaux is presenting a workshop March 31 - April 2 entitled Industrial Applications of Low Order Models Based on Proper Orthogonal Decomposition. Professor I. Michael Navon is one of the invited speakers.
The workshop will consist of 14 talks followed by open questions such as how to obtain stable and robust models with respect to parameter variations, how to decrease the projection error for physical problems including a large number of scales, or how to obtain sharp error bounds. Applications areas include flow control for the aeronautical and terrestrial vehicle industry and data assimilation in geophysics. Invited industrial partners include AIRBUS France and UK, Dassault Aviation, Boeing, Peugeot and Renault. An abstract of Professor Navon's talk is below.
POD model reduction of large scale geophysical models
Abstract: Four-dimensional variational data assimilation (4DVAR) is a powerful tool for data assimilation in meteorology and oceanography. However, a major hurdle in use of 4DVAR for realistic models is the dimension of the control space (generally equal to the size of the model state variable and typically of order 107–108) and the high computational cost in computing the cost function and its gradient requiring integration of model and its adjoint.
This led to the introduction of a reduced model approach of POD type by projecting the full model dynamics into the reduced space. Experience with a large-scale POD-based reduced model for an unstructured ocean model, the 3-D finite element Imperial College Ocean Model (ICOM) with inclusion of adaptive mesh capability is presented along with work on a ocean reduced gravity model. An adaptive POD 4-D Var is employed to update the POD bases as minimization advances and loses control. Issues of time weighting the snapshots using a dual-weighted approach to order reduction in 4D-Var Data Assimilation system tested with NASA finite volume global shallow water equations model will be discussed. Problems of suboptimal control with POD reduced model and error estimation will be addressed as well highlighting limitations of the POD approach. Finally an approach using 4-D VAR data assimilation with reduced order POD model will be outlined.