Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids
Ehimare Okoyomon, Arbel Yaniv, Christoph Goebel
TL;DR
This work systematically assesses how physics-informed inductive biases—power-flow-constrained losses, complex-valued neural networks, and residual reformulations—affect voltage prediction in heterogeneous distribution grids. Using the ENGAGE dataset, the study benchmarks in-distribution and out-of-distribution generalization for baseline and three PI variants, highlighting that complex-valued networks excel at voltage angle while physics-informed losses improve voltage magnitude robustness. Residual learning offers selective gains, but no consistently large improvements. Collectively, the results guide design choices for reliable, scalable voltage prediction in real-world distribution networks and emphasize the importance of generalization-focused evaluation.
Abstract
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.