# Gradient-Enhanced Physics-Informed Neural Networks for Power Systems Operational Support

arXiv: https://arxiv.org/abs/2206.10579 · HTML: https://mlsanity.com/paper/2206.10579/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets](https://mlsanity.com/paper/2111.01228/) (2021)
- [Efficient Database Generation for Data-driven Security Assessment of Power Systems](https://mlsanity.com/paper/1806.01074/) (2018)
- [Efficient Creation of Datasets for Data-Driven Power System Applications](https://mlsanity.com/paper/1910.01794/) (2019)
- [A Framework for Robust Assessment of Power Grid Stability and Resiliency](https://mlsanity.com/paper/1504.04684/) (2015)

## Built on by (most cited first, 6 of 6)

- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)](https://mlsanity.com/paper/2406.03172/) (2024)
- [Power Grid Behavioral Patterns and Risks of Generalization in Applied Machine Learning](https://mlsanity.com/paper/2304.10702/) (2023)
- [A comprehensive analysis of PINNs: Variants, Applications, and Challenges](https://mlsanity.com/paper/2505.22761/) (2025)
- [Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning](https://mlsanity.com/paper/2504.18091/) (2025)
- [Second-order consistency for learning chaotic dynamics via randomized Jacobian matching](https://mlsanity.com/paper/2606.01596/) (2026)

## Abstract (arXiv)

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics must be considered to ensure that the optimal solutions provided by these models adhere to practical dynamical constraints, avoiding frequency fluctuations and grid instabilities. Unfortunately, dynamic system models based on ordinary or partial differential equations are frequently unsuitable for direct application in control or state estimates due to their high computational costs. To address these challenges, this paper introduces a machine learning method to approximate the behavior of power systems dynamics in near real time. The proposed framework is based on gradient-enhanced physics-informed neural networks (gPINNs) and encodes the underlying physical laws governing power systems. A key characteristic of the proposed gPINN is its ability to train without the need of generating expensive training data. The paper illustrates the potential of the proposed approach in both forward and inverse problems in a single-machine infinite bus system for predicting rotor angles and frequency, and uncertain parameters such as inertia and damping to showcase its potential for a range of power systems applications.