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@PHDTHESIS{Wolf:992117,
      author       = {Wolf, Hinrikus},
      othercontributors = {Grohe, Martin and Schaub, Michael Thomas},
      title        = {{L}earning on graphs from theory to industrial application
                      in power management of distribution grids},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-08020},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2024},
      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.},
      cin          = {122910 / 120000},
      ddc          = {004},
      cid          = {$I:(DE-82)122910_20140620$ / $I:(DE-82)120000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-08020},
      url          = {https://publications.rwth-aachen.de/record/992117},
}