Big data and big models: On Inverse Problems that are Too Large to be Solved

In recent years large data sets have been collected and analyzed, typically, by using some machine learning algorithms. However, many types of data demand a much more in-depth analysis that requires simulation, that is, solving partial differential equations, and optimization to estimate parameters. In this talk we discuss examples for such data sets in earth science. We describe the setting in which vast amounts of geophysical data is collected from the air. We present the large scale modeling that is required to simulate such a data set and the inverse problems that arise from these types of problems. We show that by using traditional techniques these problems cannot be solved in reasonable time on reasonable hardware. We then discuss a new set of algorithms that enable us to solve such problems. These algorithms are based on a concept we call domain of interest computation for the forward coupled with stochastic programming for the inverse. We show that by using this combination we are able to solve very large scale inverse problems, using a rather modest hardware in reasonable time.