# High-Fidelity Machine Learning Approximations of Large-Scale Optimal Power Flow

arXiv: https://arxiv.org/abs/2006.16356 · HTML: https://mlsanity.com/paper/2006.16356/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

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

- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimization](https://mlsanity.com/paper/2105.08881/) (2021)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets](https://mlsanity.com/paper/2111.01228/) (2021)
- [Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments](https://mlsanity.com/paper/2211.15755/) (2022)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality](https://mlsanity.com/paper/2212.03977/) (2022)
- [Sobolev Training of End-to-End Optimization Proxies](https://mlsanity.com/paper/2505.11342/) (2025)
- [Diffusion-based learning framework for Constrained Nonconvex Optimization with Weighted Bootstrapped Refinement](https://mlsanity.com/paper/2502.10330/) (2025)
- [The intersection of machine learning with forecasting and optimisation: theory and applications](https://mlsanity.com/paper/2211.13583/) (2022)

## Abstract (arXiv)

The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational constraints. It is non-convex and NP-hard, and computationally challenging for large-scale power systems. Motivated by the increased stochasticity in generation schedules and increasing penetration of renewable sources, this paper explores a deep learning approach to deliver highly efficient and accurate approximations to the AC-OPF. In particular, the paper proposes an integration of deep neural networks and Lagrangian duality to capture the physical and operational constraints. The resulting model, called OPF-DNN, is evaluated on real case studies from the French transmission system, with up to 3,400 buses and 4,500 lines. Computational results show that OPF-DNN produces highly accurate AC-OPF approximations whose costs are within 0.01% of optimality. OPF-DNN generates, in milliseconds, solutions that capture the problem constraints with high fidelity.