Inverse Problems and Uncertainty Quantification: A Gentle Introduction
Brian Zaharatos
Department of Applied Mathematics and Statistics, Colorado School of Mines
Date and time:
Thursday, April 2, 2015 - 12:00pm
Location:
ECCR 257
Abstract:
In science and engineering, it is often assumed that a mathematical model describes the relationship between a set of physical model parameters and observable data. Computing data values given a set of unknown parameters is called the “forward problem”. However, practitioners are often concerned with the “inverse problem”, i.e., learning about unknown physical parameters through observations of data. Further, if data are measured with random error, then it is often desirable for practitioners to quantify how this measurement error affects their estimates of model parameters. In this talk, we will attempt to get a better understanding of the forward and inverse problems using simple examples from the calculus sequence. Then, with these concepts in mind, we will look at a real-world inverse problem: learning about key performance parameters of a solar cell (e.g., the maximum power output) from noisy laboratory measurements. The goal of this talk is to describe an area of active mathematical and statistical research at a level that an undergraduate student can appreciate. Such descriptions are important because they give undergraduate students a chance to see the excitement and complexity of a current research project without feeling overwhelmed with technical details.