Ehimare Okoyomon

Syed Zain Abbas, Ehimare Okoyomon

To address the lack of public power system data for machine learning research in energy networks, we investigate the use of variational graph autoencoders (VGAEs) for synthetic distribution grid generation. Using two open-source datasets, ENGAGE and DINGO, we evaluate four decoder variants and compare generated networks against the original grids using structural and spectral metrics. Results indicate that simple decoders fail to capture realistic topologies, while GCN-based approaches achieve strong fidelity on ENGAGE but struggle on the more complex DINGO dataset, producing artifacts such as disconnected components and repeated motifs. These findings highlight both the promise and limitations of VGAEs for grid synthesis, underscoring the need for more expressive generative models and robust evaluation. We release our models and analysis as open source to support benchmarking and accelerate progress in ML-driven power system research.

Ehimare Okoyomon, Christoph Goebel

Accurate power flow analysis is critical for modern distribution systems, yet classical solvers face scalability issues, and current machine learning models often struggle with generalization. We introduce BOOST-RPF, a novel method that reformulates voltage prediction from a global graph regression task into a sequential path-based learning problem. By decomposing radial networks into root-to-leaf paths, we leverage gradient-boosted decision trees (XGBoost) to model local voltage-drop regularities. We evaluate three architectural variants: Absolute Voltage, Parent Residual, and Physics-Informed Residual. This approach aligns the model architecture with the recursive physics of power flow, ensuring size-agnostic application and superior out-of-distribution robustness. Benchmarked against the Kerber Dorfnetz grid and the ENGAGE suite, BOOST-RPF achieves state-of-the-art results with its Parent Residual variant which consistently outperforms both analytical and neural baselines in standard accuracy and generalization tasks. While global Multi-Layer Perceptrons (MLPs) and Graph Neural Networks (GNNs) often suffer from performance degradation under topological shifts, BOOST-RPF maintains high precision across unseen feeders. Furthermore, the framework displays linear $O(N)$ computational scaling and significantly increased sample efficiency through per-edge supervision, offering a scalable and generalizable alternative for real-time distribution system operator (DSO) applications.

Martin Carrasco, Caio F. Deberaldini Netto, Vahan A. Martirosyan et al.

The expressive power of graph neural networks (GNNs) is typically understood through their correspondence with graph isomorphism tests such as the Weisfeiler-Leman (WL) hierarchy. While more expressive GNNs can distinguish a richer set of graphs, they are also observed to suffer from higher generalization error. This work provides a theoretical explanation for this trade-off by linking expressivity and generalization through the lens of coloring algorithms. Specifically, we show that the number of equivalence classes induced by WL colorings directly bounds the GNNs Rademacher complexity -- a key data-dependent measure of generalization. Our analysis reveals that greater expressivity leads to higher complexity and thus weaker generalization guarantees. Furthermore, we prove that the Rademacher complexity is stable under perturbations in the color counts across different samples, ensuring robustness to sampling variability across datasets. Importantly, our framework is not restricted to message-passing GNNs or 1-WL, but extends to arbitrary GNN architectures and expressivity measures that partition graphs into equivalence classes. These results unify the study of expressivity and generalization in GNNs, providing a principled understanding of why increasing expressive power often comes at the cost of generalization.

Ehimare Okoyomon, Arbel Yaniv, Christoph Goebel

Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor generalization when trained on limited or incomplete data. In this work, we systematically investigate the role of inductive biases in improving a model's ability to reliably learn power flow. Specifically, we evaluate three physics-informed strategies: (i) power-flow-constrained loss functions, (ii) complex-valued neural networks, and (iii) residual-based task reformulation. Using the ENGAGE dataset, which spans multiple low- and medium-voltage grid configurations, we conduct controlled experiments to isolate the effect of each inductive bias and assess both standard predictive performance and out-of-distribution generalization. Our study provides practical insights into which model assumptions most effectively guide learning for reliable and efficient voltage prediction in modern distribution networks.