# Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility

arXiv: https://arxiv.org/abs/2303.08994 · HTML: https://mlsanity.com/paper/2303.08994/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 15 Mar 2023.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Solving Power System Differential Algebraic Equations Using Differential Transformation](https://mlsanity.com/paper/1903.00935/) (2019)
- [A Time-Power Series Based Semi-Analytical Approach for Power System Simulation](https://mlsanity.com/paper/1804.07330/) (2018)

## Built on by (most cited first, 13 of 13)

- [PINNSim: A Simulator for Power System Dynamics based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2303.10256/) (2023)
- [Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators](https://mlsanity.com/paper/2410.24162/) (2024)
- [Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.01340/) (2024)
- [Correctness Verification of Neural Networks Approximating Differential Equations](https://mlsanity.com/paper/2402.07621/) (2024)
- [Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks](https://mlsanity.com/paper/2502.08783/) (2025)
- [PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems](https://mlsanity.com/paper/2507.06712/) (2025)
- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Enhanced physics-informed neural networks (PINNs) for high-order power grid dynamics](https://mlsanity.com/paper/2410.07527/) (2024)
- [UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations](https://mlsanity.com/paper/2603.10466/) (2026)
- [Multi-dimensional training-priority weighting based on physical information propagation paths: a unified residual-weighting framework for physics-informed neural networks](https://mlsanity.com/paper/2607.11094/) (2026)
- [Event-Structured Physics-Informed Neural Networks for Differentiable Critical Clearing Boundaries](https://mlsanity.com/paper/2607.27681/) (2026)
- [Tools to Explain Neural Networks for Power System Dynamics](https://mlsanity.com/paper/2608.08048/) (2026)
- [From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?](https://mlsanity.com/paper/2609.33387/) (2026)

## Abstract (arXiv)

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power systems. Physics-Informed Neural Networks (PINNs) have recently emerged as a promising solution for drastically accelerating computations of non-linear dynamical systems. This work investigates the applicability of these methods for power system dynamics, focusing on the dynamic response to load disturbances. Comparing the prediction of PINNs to the solution of conventional solvers, we find that PINNs can be 10 to 1000 times faster than conventional solvers. At the same time, we find them to be sufficiently accurate and numerically stable even for large time steps. To facilitate a deeper understanding, this paper also present a new regularisation of Neural Network (NN) training by introducing a gradient-based term in the loss function. The resulting NNs, which we call dtNNs, help us deliver a comprehensive analysis about the strengths and weaknesses of the NN based approaches, how incorporating knowledge of the underlying physics affects NN performance, and how this compares with conventional solvers for power system dynamics.