Practical Improvement to and Application of Proper Orthogonal Decomposition Reduced Order Modeling to Experimental Design for Groundwater Monitoring Networks

摘要

Proper Orthogonal Decomposition (POD) is a method used to reduce the dimension of a highly discretized groundwater model. The reduced model is sometimes several orders of magnitudes smaller than the original model and can run several orders of magnitude faster. The key advantage of utilizing a POD reduced model is its ability to drastically reduce the computational burden of repeated model calls, which are required in Monte Carlo simulation, uncertainty analysis, and heuristically searched experimental design. Although POD has been applied to many areas of research, there continues to be room to improve its implementation. This dissertation consists of six chapters. After an introductory chapter, the second chapter discusses a method that can be used to improve the efficiency of constructing complex POD reduced models. The third through fifth chapters develops methodologies by which POD reduced models are used to solve the experimental design problem of optimizing a network of observation wells to gain information about the modeled aquifer. The final chapter offers some conclusions, discussions, and potential future research opportunities.