Model Reduction in Groundwater Modeling

Abstract:

Model reduction has been shown to be a very effective method for reducing the computational burden of large-scale simulations. Model reduction techniques preserve much of the physical knowledge of the system and primarily seek to remove components from the model that do not provide significant information of interest. Proper Orthogonal Decomposition (POD) is a model reduction technique by which a system of ordinary equations is projected onto a much smaller subspace in such a way that the span of the subspace is equal to the span of the original full model space. Basically, the POD technique selects a small number of orthonormal basis functions (principal components) that span the spatial variability of the solutions. In this way the state variable (head) is approximated by a linear combination of these basis functions and, using a Galerkin projection, the dimension of the problem is significantly reduced. It has been shown that for a highly discritized model, the reduced model can be two to three orders of magnitude smaller than the original model and runs 1,000 faster. More importantly, the reduced model captures the dominating characteristics of the full model and produces sufficiently accurate solutions. One of the major tasks in the development of the reduced model is the selection of snapshots which are used to determine the dominant eigenvectors. This paper discusses ways to optimize the snapshot selection. Additionally, the paper also discusses applications of the reduced model to parameter estimation, Monte Carlo simulation and experimental design in groundwater modeling.