Don Estep will be visiting the CTL group in March 20th and will give a seminar on that day. The topic is “Stochastic Inverse Problems for Parameter Determination”. See below for an abstract. The seminar is between 14-15 in the Visualisation Studio on the fourth floor in the D-building.

Abstract. A mathematical model of a physical system determines a map between the parameter and data values characterizing the properties of a particular system and the output quantities describing the behavior of the system. In many cases, we can make observations of the behavior of the system, but the parameter and data values cannot be observed directly. This raises the inverse problem of determining the possible parameter/data values that correspond to given observations. A defining characteristic of this inverse problem is that the solutions are set-valued or equivalence classes, since in general multiple parameter values can yield the same output value. Moreover, since observation data generally has a stochastic nature, the solution of the inverse problem is described as a probability measure.

We describe recent work on the formulation, solution, and uncertainty quantification for the parameter identification problem. This new approach has two stages: a systematic way to approximate set-valued solutions of inverse problems and the use of measure theoretic techniques for approximating probability distributions in parameter space. We also carry out an error analysis for uncertainty quantification. We will also describe some current work and the relation to other inverse problems such as data assimilation.