Optimal Diagram Representations of Polycrystalline Microstructures.

17^th October 2023, 14:00
Andreas Alpers
Mathematical Sciences

Abstract

Voronoi diagrams and their generalizations, particularly so-called generalized balanced power diagrams (GBPDs), are increasingly used to represent grain shapes of polycrystalline materials at the microstructural scale. These diagrams can be described by few parameters and, in principle, only these parameters need to be recovered from tomographic measurements. Experimentalists have reported, however, that some parameters seem more important than others for describing certain families of materials. In this talk, I will focus on this finding and will provide some theoretical explanations within the framework of statistical learning theory. I will also discuss how the task of finding an optimal set of parameters can be formulated and solved via a support vector machine approach. (The talk is based on recent joint work with P. Gritzmann, M. Fiedler, and F. Klemm.)