# Global Performance Guarantees for Neural Network Models of AC Power Flow

arXiv: https://arxiv.org/abs/2211.07125 · HTML: https://mlsanity.com/paper/2211.07125/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 14 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming](https://mlsanity.com/paper/2010.11645/) (2020)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations](https://mlsanity.com/paper/1711.01728/) (2017)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2003.07939/) (2020)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Fast Power system security analysis with Guided Dropout](https://mlsanity.com/paper/1801.09870/) (2018)
- [Proving Global Optimality of ACOPF Solutions](https://mlsanity.com/paper/1910.03716/) (2019)
- [Optimization-Based Exploration of the Feasible Power Flow Space for Rapid Data Collection](https://mlsanity.com/paper/2206.12214/) (2022)

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

- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [GPU-Accelerated Verification of Machine Learning Models for Power Systems](https://mlsanity.com/paper/2306.10617/) (2023)
- [Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow](https://mlsanity.com/paper/2405.06109/) (2024)
- [Achieving the Tightest Relaxation of Sigmoids for Formal Verification](https://mlsanity.com/paper/2408.10491/) (2024)

## Abstract (arXiv)

Machine learning, which can generate extremely fast and highly accurate black-box surrogate models, is increasingly being applied to a variety of AC power flow problems. Rigorously verifying the accuracy of the resulting black-box models, however, is computationally challenging. This paper develops a tractable neural network verification procedure which incorporates the ground truth of the non-linear AC power flow equations to determine worst-case neural network prediction error. Our approach, termed Sequential Targeted Tightening (STT), leverages a loosely convexified reformulation of the original verification problem, which is an intractable mixed integer quadratic program (MIQP). Using the sequential addition of targeted cuts, we iteratively tighten our formulation until either the solution is sufficiently tight or a satisfactory performance guarantee has been generated. After learning neural network models of the 14, 57, 118, and 200-bus PGLib test cases, we compare the performance guarantees generated by our STT procedure with ones generated by a state-of-the-art MIQP solver, Gurobi 11.0. We show that STT often generates performance guarantees which are far tighter than the MIQP upper bound.