# Transient Stability Analysis with Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2106.13638 · HTML: https://mlsanity.com/paper/2106.13638/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 25 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [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)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [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)
- [Lyapunov Functions Family Approach to Transient Stability Assessment](https://mlsanity.com/paper/1409.1889/) (2014)

## Built on by (most cited first, 5 of 5)

- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Physics Informed Neural Networks for Phase Locked Loop Transient Stability Assessment](https://mlsanity.com/paper/2303.12116/) (2023)
- [IRMAC: Interpretable Refined Motifs in Binary Classification for Smart Grid Applications](https://mlsanity.com/paper/2109.13732/) (2021)
- [PINNs-Based Uncertainty Quantification for Transient Stability Analysis](https://mlsanity.com/paper/2311.12947/) (2023)
- [Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation](https://mlsanity.com/paper/2508.21559/) (2025)

## Abstract (arXiv)

We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment, the traditionally applied methods either carry a significant computational burden, require model simplifications, or use overly conservative surrogate models. Conventional neural networks can circumvent these limitations but are faced with high demand of high-quality training datasets, while they ignore the underlying governing equations. Physics-informed neural networks are different: they incorporate the power system differential algebraic equations directly into the neural network training and drastically reduce the need for training data. This paper takes a deep dive into the performance of physics-informed neural networks for power system transient stability assessment. Introducing a new neural network training procedure to facilitate a thorough comparison, we explore how physics-informed neural networks compare with conventional differential-algebraic solvers and classical neural networks in terms of computation time, requirements in data, and prediction accuracy. We illustrate the findings on the Kundur two-area system, and assess the opportunities and challenges of physics-informed neural networks to serve as a transient stability analysis tool, highlighting possible pathways to further develop this method.