Parameter Estimation for some Geoscience Applications using a Measure-Theoretic Approach
Professor, Department Associate Chair, Head of Computational Hydraulics
The University of Texas at Austin
Effective modeling of complex physical systems arising in the geosciences is dependent on knowing parameters which are often difficult or impossible to measure in situ. In this talk we focus on two such problems, estimating parameters for groundwater flow and contaminant transport, and estimating parameters within a coastal ocean model. The approach we will describe, proposed by collaborators D. Estep, T. Butler and others, is based on measure-theoretic stochastic inversion technique. In this approach, given a probability space on certain observable quantities of interest, one searches for the sets of highest probability in parameter space that give rise to these observables. When viewed as mappings between sets, the stochastic inversion problem is well-posed in certain settings, but there are computational challenges related to the set construction. We will focus the talk on estimating scalar parameters and fields in a contaminant transport setting, and in estimating bottom friction in a complicated near-shore coastal application. The talk is joint work with M. Vesselinov at LANL, D. Estep at Colorado State University, T. Butler at U. Colorado Denver, S. Mattis from TU Munich, L. Graham from Amazon Web Services, and J. He and S. Estes from UT Austin, and the work is funded by DOE, NSF and ExxonMobil.