Scientific Computing Group Seminars - Detail View

Speaker: D. Estep

Affiliation: Colorado State University

Talk Title: A Measure Theoretic Computational Approach For Inverse Sensitivity Problems

Invited by: Jan S Hesthaven

Time: March 26 2010 11 a.m.

Location: 182 George Street, Room 110

Abstract:

We describe a computational method for probabilistic inverse sensitivity analysis of a map from a set of parameters and data to a computed quantity of interest. The inverse problem is to describe the random variation in the input and parameters that lead to an imposed or observed random variation on the output quantity. To complicate matters, we are interested in implicitly-defined maps, such as a quantity of interest computed from the solution of a differential equation. We formulate the problem as an ill-posed inverse problem for an integral equation using the Law of Total Probability and then describe a computational method for computing solutions. The method has two stages. In the first part, we approximate the unique set-valued solution to the inverse of the integral equation using derivative information. In the second part, we apply basic ideas from measure theory to compute the approximate probability measure on the parameter and data space that solves the integral equation. We discuss convergence of the method, and explain how to use the method to compute the probability of events in the input (parameter) space. The talk is illustrated with a number of examples. Time permitting, we discuss briefly the numerical analysis (accuracy) of the method and the consideration of multiple quantities of interest and data assimilation.