# Physics-Informed Gradient Estimation for Accelerating Deep Learning based AC-OPF

arXiv: https://arxiv.org/abs/2502.16373 · HTML: https://mlsanity.com/paper/2502.16373/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee](https://mlsanity.com/paper/2512.11127/) (2025)
- [Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies](https://mlsanity.com/paper/2606.03125/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)

## Abstract (arXiv)

The optimal power flow (OPF) problem can be rapidly and reliably solved by employing responsive online solvers based on neural networks. The dynamic nature of renewable energy generation and the variability of power grid conditions necessitate frequent neural network updates with new data instances. To address this need and reduce the time required for data preparation time, we propose a semi-supervised learning framework aided by data augmentation. In this context, ridge regression replaces the traditional solver, facilitating swift prediction of optimal solutions for the given input load demands. Additionally, to accelerate the backpropagation during training, we develop novel batch-mean gradient estimation approaches along with a reduced branch set to alleviate the complexity of gradient computation. Numerical simulations demonstrate that our neural network, equipped with the proposed gradient estimators, consistently achieves feasible and near-optimal solutions. These results underline the effectiveness of our approach for practical implementation in real-time OPF applications.