Abstract

In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since be-come important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples.

About Prof. Martin Stoll

Prof. Martin Stoll received a PhD in numerical analysis from University of Oxford. Then he worked as a postdoctoral researcher in Oxford and MPI Magdeburg Germany. He became a research group leader (W2) at MPI Magdeburg in 2013 and took the professorship for scientific computing at Technische Universität Chemnitz since 2017. Martin does research in Numerical Linear Algebra and everything that comes with it. I like large-scale PDE-constrained optimization, discretization of PDEs, phase field problems and their applications as well as really cool data science applications. He started the GAMM activities group in Computational and Mathematical Methods in Data Science (COMinDS).