Lehrveranstaltungen
Aktuelle Lehrveranstaltungen: Sommersemester 2024
Machine Learning with Graphs (Masterseminar)
Dozenten: Prof. Dr. Leon Bungert, Dr. Eloi Martinet
In this seminar we will discover machine learning methods that involve graphs. This includes partial differential equations on graphs and their use for semi-supervised machine learning, as well as graph neural networks for supervised learning with graph data. The seminar will cover theoretical and numerical aspects and can lead to a master's thesis in this topic.
For any questions, please feel free to contact leon.bungert@uni-wuerzburg.de. I look forward to your interest!
2 St. Mi 10-12 S0. 101
Referenzen:
[1] Calder, J., Cook, B., Thorpe, M., & Slepcev, D. (2020, November). Poisson learning: Graph based semi-supervised learning at very low label rates. In International Conference on Machine Learning (pp. 1306-1316). PMLR.
[2] Calder, J. (2018). The game theoretic p-Laplacian and semi-supervised learning with few labels. Nonlinearity, 32(1), 301.
[3] Bungert, L., Calder, J., & Roith, T. (2023). Uniform convergence rates for Lipschitz learning on graphs. IMA Journal of Numerical Analysis, 43(4), 2445-2495.
[4] Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017). Geometric deep learning: going beyond euclidean data. IEEE Signal Processing Magazine, 34(4), 18-42.
[5] Bronstein, M. M., Bruna, J., Cohen, T., & Veličković, P. (2021). Geometric deep learning: Grids, groups, graphs, geodesics, and gauges. arXiv preprint arXiv:2104.13478.
[6] Xia, F., Sun, K., Yu, S., Aziz, A., Wan, L., Pan, S., & Liu, H. (2021). Graph learning: A survey. IEEE Transactions on Artificial Intelligence, 2(2), 109-127.
[7] Song, Z., Yang, X., Xu, Z., & King, I. (2022). Graph-based semi-supervised learning: A comprehensive review. IEEE Transactions on Neural Networks and Learning Systems.
Mathematical Foundations of Data Science II (2+1 im Bachelor Mathematical Data Science)
Dozent: Prof. Leon Bungert
Die Vorlesung "Mathematical Foundations of Data Science" behandelt die wesentlichen mathematischen Konzepte, die für das Verständnis und die Anwendung von Data Science und maschinellem Lernen unerlässlich sind. Hierzu gibt es Einführungen in grundlegende mathematische Konzepte der lineare Algebra und und Statistik. Zudem werden spezifische mathematische Techniken und Methoden vorgestellt, die in der Datenanalyse und maschinellen Lernverfahren verwendet werden. Dazu gehören Optimierung, numerische Methoden, lineare Regression, Clusteranalyse, Dimensionsreduktion, künstliche neuronale Netze und Deep Learning. Die Vorlesung konzentriert sich darauf, den Studierenden die grundlegenden Methoden und Konzepte der Datenwissenschaften zu erlernen und sie für Anwendungen einzusetzen. Wenden Sie sich bei Fragen gerne per Email an leon.bungert@uni-wuerzburg.de. Ich freue mich über Ihr Interesse!
2 St. Di 10-12, SE 40.01.003
Übung zu Mathematical Foundations of Data Science II
Mo 12-14, SE 40.03.003
Numerische Mathematik und Angewandte Analysis (Arbeitsgemeinschaft)
Dozent: Dr. Eloi Martinet
4St. Mo 16-18 S0 102, Mi 8-10 S0. 107
In the vast majority of theoretical and real-world applications, the solution to a partial differential equation can not be computed analytically. The aim of this course is to explore two methods allowing to compute approximate solutions. The first, ”traditional” one, is the Finite Element Method. The second one makes use of the recent developments in Deep Learning leading to the so called ”Physics Informed Neural Networks”. In a first part, we will study the fundamental tools needed to solves elliptic partial differential equations, such as weak derivatives and Sobolev spaces. We will show how to approximate PDEs using basic finite elements tools. In the second part, we present the definition of au Neural Network and derive the proof of the so-called "Universal Approximation Theorem". Using backpropagation, we show how a network can be trained to solve some partial differential equations.
For any questions, please feel free to contact eloi.martinet@uni-wuerzburg.de. I look forward to your interest!
