# Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks

arXiv: https://arxiv.org/abs/2006.11029 · HTML: https://mlsanity.com/paper/2006.11029/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 28 of 28)

- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments](https://mlsanity.com/paper/2211.15755/) (2022)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Data-Driven Time Series Reconstruction for Modern Power Systems Research](https://mlsanity.com/paper/2110.13772/) (2021)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks](https://mlsanity.com/paper/2310.04605/) (2023)
- [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)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)
- [Efficient and Robust Mixed-Integer Optimization Methods for Training Binarized Deep Neural Networks](https://mlsanity.com/paper/2110.11382/) (2021)
- [Global Performance Guarantees for Neural Network Models of AC Power Flow](https://mlsanity.com/paper/2211.07125/) (2022)
- [GPU-Accelerated Verification of Machine Learning Models for Power Systems](https://mlsanity.com/paper/2306.10617/) (2023)
- [Minimizing Worst-Case Violations of Neural Networks](https://mlsanity.com/paper/2212.10930/) (2022)
- [Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow](https://mlsanity.com/paper/2206.01864/) (2022)
- [Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization](https://mlsanity.com/paper/2306.06674/) (2023)
- [Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow](https://mlsanity.com/paper/2405.06109/) (2024)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [Wasserstein Distributionally Robust Shallow Convex Neural Networks](https://mlsanity.com/paper/2407.16800/) (2024)
- [Analytical Verification of Performance of Deep Neural Network Based Time-Synchronized Distribution System State Estimation](https://mlsanity.com/paper/2311.06973/) (2023)
- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees](https://mlsanity.com/paper/2303.13228/) (2023)
- [AI Driven Near Real-time Locational Marginal Pricing Method: A Feasibility and Robustness Study](https://mlsanity.com/paper/2306.10080/) (2023)
- [Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids](https://mlsanity.com/paper/2605.23194/) (2026)
- [Finite-Sample Probabilistic Safety Certification for AI-Based Grid-Edge Coordination](https://mlsanity.com/paper/2609.28182/) (2026)

## Abstract (arXiv)

This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.