# Adaptive Informed Deep Neural Networks for Power Flow Analysis

arXiv: https://arxiv.org/abs/2412.02659 · HTML: https://mlsanity.com/paper/2412.02659/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 56 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 23 of 23)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (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-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach](https://mlsanity.com/paper/2006.00544/) (2020)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach](https://mlsanity.com/paper/1906.06017/) (2019)
- [Physics-informed Graphical Neural Network for Power System State Estimation](https://mlsanity.com/paper/2312.17738/) (2023)
- [Learning the Optimal Power Flow: Environment Design Matters](https://mlsanity.com/paper/2403.17831/) (2024)
- [Physics-Informed Neural Networks for Accelerating Power System State Estimation](https://mlsanity.com/paper/2310.03088/) (2023)
- [Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation](https://mlsanity.com/paper/2301.03766/) (2023)
- [Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow](https://mlsanity.com/paper/2206.01864/) (2022)
- [Physics-Guided Graph Neural Networks for Real-time AC/DC Power Flow Analysis](https://mlsanity.com/paper/2305.00216/) (2023)
- [GPU-Resident Sparse Direct Linear Solvers for Alternating Current Optimal Power Flow Analysis](https://mlsanity.com/paper/2306.14337/) (2023)
- [Quantum Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2311.06293/) (2023)
- [Adaptive Power Flow Approximations with Second-Order Sensitivity Insights](https://mlsanity.com/paper/2404.04391/) (2024)
- [Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations](https://mlsanity.com/paper/2404.17541/) (2024)

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

- [Physics-Informed Reinforcement Learning for Large-Scale EV Smart Charging Considering Distribution Network Voltage Constraints](https://mlsanity.com/paper/2510.12335/) (2025)

## Abstract (arXiv)

This study introduces PINN4PF, an end-to-end deep learning architecture for power flow (PF) analysis that effectively captures the nonlinear dynamics of large-scale modern power systems. The proposed neural network (NN) architecture consists of two important advancements in the training pipeline: (A) a double-head feed-forward NN that aligns with PF analysis, including an activation function that adjusts to the net active and reactive power injections patterns, and (B) a physics-based loss function that partially incorporates power system topology information through a novel hidden function. The effectiveness of the proposed architecture is illustrated through 4-bus, 15-bus, 290-bus, and 2224-bus test systems and is evaluated against two baselines: a linear regression model (LR) and a black-box NN (MLP). The comparison is based on (i) generalization ability, (ii) robustness, (iii) impact of training dataset size on generalization ability, (iv) accuracy in approximating derived PF quantities (specifically line current, line active power, and line reactive power), and (v) scalability. Results demonstrate that PINN4PF outperforms both baselines across all test systems by up to two orders of magnitude not only in terms of direct criteria, e.g., generalization ability, but also in terms of approximating derived physical quantities.