# Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids

arXiv: https://arxiv.org/abs/2509.25158 · HTML: https://mlsanity.com/paper/2509.25158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [Physics-Aware Neural Networks for Distribution System State Estimation](https://mlsanity.com/paper/1903.09669/) (2019)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI](https://mlsanity.com/paper/2208.08485/) (2022)
- [PowerGNN: A Topology-Aware Graph Neural Network for Electricity Grids](https://mlsanity.com/paper/2503.22721/) (2025)
- [Physics-guided Residual Learning for Probabilistic Power Flow Analysis](https://mlsanity.com/paper/2301.12062/) (2023)

## Built on by (most cited first, 1 of 1)

- [BOOST-RPF: Boosted Sequential Trees for Radial Power Flow](https://mlsanity.com/paper/2603.21977/) (2026)

## Abstract (arXiv)

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.