Efficient Modeling of Data Intensive Inverse Problems Using Wavelet-based Prioritization Techniques

We describe various wavelet-based prioritization techniques that lead to efficient models for data intensive inverse problems commonly arising in engineering applications. Computer simulations of physical processes that are governed by differential or integral equations often involve thousands or even millions of unknown variables, especially if the problem is geometrically complex and multidimensional in nature. Our goal is to effectively manage the large amounts of data that are generated by such simulations and hence control the associated memory and computational costs. By focusing on finding a good data representation before attempting to build the engineering model, we demonstrate that we can efficiently solve problems that have previously pushed the limits of computing technology. We present examples that illustrate the savings that can be obtained by conditioning and compressing large matrices arising from inverse problems defined on general 3D domains.