# Physics-Guided Deep Neural Networks for Power Flow Analysis

arXiv: https://arxiv.org/abs/2002.00097 · HTML: https://mlsanity.com/paper/2002.00097/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 30 of 33)

- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Physically Consistent Neural Networks for building thermal modeling: theory and analysis](https://mlsanity.com/paper/2112.03212/) (2021)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Network](https://mlsanity.com/paper/2201.10967/) (2022)
- [Physics-Informed Convolutional Autoencoder for Cyber Anomaly Detection in Power Distribution Grids](https://mlsanity.com/paper/2312.04758/) (2023)
- [Global Performance Guarantees for Neural Network Models of AC Power Flow](https://mlsanity.com/paper/2211.07125/) (2022)
- [Physics-Informed Autonomous LLM Agents for Explainable Power Electronics Modulation Design](https://mlsanity.com/paper/2411.14214/) (2024)
- [Learning Power Flow with Confidence: A Probabilistic Guarantee Framework for Voltage Risk](https://mlsanity.com/paper/2308.07867/) (2023)
- [Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator](https://mlsanity.com/paper/2509.22458/) (2025)
- [Domain-guided Machine Learning for Remotely Sensed In-Season Crop Growth Estimation](https://mlsanity.com/paper/2106.13323/) (2021)
- [Machine Learning for Naval Architecture, Ocean and Marine Engineering](https://mlsanity.com/paper/2109.05574/) (2021)
- [Towards Practical Physics-Informed ML Design and Evaluation for Power Grid](https://mlsanity.com/paper/2205.03673/) (2022)
- [Power Grid Behavioral Patterns and Risks of Generalization in Applied Machine Learning](https://mlsanity.com/paper/2304.10702/) (2023)
- [MODL: Multilearner Online Deep Learning](https://mlsanity.com/paper/2405.18281/) (2024)
- [Robustness Analysis of AI Models in Critical Energy Systems](https://mlsanity.com/paper/2406.14361/) (2024)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)
- [SenseFlow: A Physics-Informed and Self-Ensembling Iterative Framework for Power Flow Estimation](https://mlsanity.com/paper/2505.12302/) (2025)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [Parameter-Efficient Domain Adaptation of Physics-Informed Self-Attention based GNNs for AC Power Flow Prediction](https://mlsanity.com/paper/2602.18227/) (2026)
- [Exploration of Artificial Intelligence-oriented Power System Dynamic Simulators](https://mlsanity.com/paper/2110.00931/) (2021)
- [Semi-supervised physics guided deep learning framework for predicting the I-V characteristics of GAN HEMT](https://mlsanity.com/paper/2110.10724/) (2021)
- [Robust, Deep, and Reinforcement Learning for Management of Communication and Power Networks](https://mlsanity.com/paper/2202.05395/) (2022)
- [Emission-Aware Optimization of Gas Networks: Input-Convex Neural Network Approach](https://mlsanity.com/paper/2209.08645/) (2022)
- [Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes](https://mlsanity.com/paper/2504.21260/) (2025)
- [Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation](https://mlsanity.com/paper/2508.21559/) (2025)
- [Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit](https://mlsanity.com/paper/2509.03495/) (2025)
- [Rebuild AC Power Flow Models with Graph Attention Networks](https://mlsanity.com/paper/2509.22733/) (2025)
- [Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow](https://mlsanity.com/paper/2511.11677/) (2025)
- [Scale-Adaptive Power Flow Analysis with Local Topology Slicing and Multi-Task Graph Learning](https://mlsanity.com/paper/2601.01387/) (2026)

## Abstract (arXiv)

Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable due to system dynamics and uncertainties, making traditional numerical approaches infeasible. To address these concerns, researchers have proposed data-driven approaches to solve the PF problem by learning the mapping rules from historical system operation data. Nevertheless, prior data-driven approaches suffer from poor performance and generalizability, due to overly simplified assumptions of the PF problem or ignorance of physical laws governing power systems. In this paper, we propose a physics-guided neural network to solve the PF problem, with an auxiliary task to rebuild the PF model. By encoding different granularity of Kirchhoff's laws and system topology into the rebuilt PF model, our neural-network based PF solver is regularized by the auxiliary task and constrained by the physical laws. The simulation results show that our physics-guided neural network methods achieve better performance and generalizability compared to existing unconstrained data-driven approaches. Furthermore, we demonstrate that the weight matrices of our physics-guided neural networks embody power system physics by showing their similarities with the bus admittance matrices.