+********************************************************************** * * * Einladung * * * * Informatik-Oberseminar * * * +********************************************************************** Zeit: Donnerstag, 08. August 2024, 10:00 - 11:00 Uhr Ort: Raum 9222 (großer Seminarraum, Erweiterungsbau 3, Informatikzentrum, Ahornstraße 55) Referent: Herr Hinrikus Eike Wolf, M. Sc. Lehrstuhl Logik und Theorie diskreter Systeme (Informatik 7) Thema: Learning on Graphs from Theory to Industrial Application in Power Management of Distribution Grids Abstract: Learning on graphs has strong ties to theoretical computer science, as some algorithms used for learning are rooted in graph theory. Furthermore, expressivity of learning methods is analysed with techniques from theoretical computer science. From a practical perspective, graph learning finds application in a wide range of domains, such as biochemistry, social science, and in case of this thesis in power management of electric grids. An illustrative example for graph learning is to predict whether a chemical molecule is toxic or non-toxic. The task behind this example involves predicting properties of the whole graph. Beyond this, graph learning includes also to node level tasks, and link prediction. We propose structural node embeddings motivated from Lovasz' (1967) theory of graph homomorphism counts. These are the number of mappings from Graph H to G such that vertices which are adjacent in H are also adjacent in G. The node embeddings consist of vectors representing homomorphism counts from families of graphs within the graph to be embedded. We showcase that our approach achieves comparable accuracy to other methods on benchmark data, except for recent GNN architectures. We conduct a study of the stability of node embeddings across five prominent methods. Most embedding techniques inherently depend on randomness. We analyse the effects of this randomness on the embeddings themselves and on downstream tasks, uncovering significant instabilities, particularly in individual predictions. This finding is crucial for practitioners in selecting an embedding method that meets the requirements of their tasks. We present a GNN architecture for the AC Power Flow problem, which helps detect congestion in AC (alternating current) grids. The AC Power Flow is a non-linear, complex optimization problem without a closed-form solution and is typically addressed using Newton's iterative method. Experimentally, we demonstrate that our method is able to generalize to unknown grids. While the model is better than previous neural approaches, it is not accurate enough to replace classical solvers. We introduce a deep reinforcement learning architecture that can resolve congestion detected by AC Power Flow computation. Congestions appear more often in electric grids, due to the increasing number of electric vehicles, heatpumps, and photovoltaic systems. As in contemporary grids measuring infrastructure is only sparsely available, our architecture learns from this sparse data to resolve the congestions. We demonstrate the ability of our method by experiments on a real-world low voltage grid. Our approach matches accuracy of state-of-the-art classical solvers, with the distinct advantage of being orders of magnitude faster. Es laden ein: die Dozentinnen und Dozenten der Informatik