# Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

arXiv: https://arxiv.org/abs/1910.01624 · HTML: https://mlsanity.com/paper/1910.01624/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 26 of 26)

- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planes](https://mlsanity.com/paper/2501.00200/) (2024)
- [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)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verification](https://mlsanity.com/paper/2512.11087/) (2025)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Verifying Quantized Neural Networks using SMT-Based Model Checking](https://mlsanity.com/paper/2106.05997/) (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)
- [Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation](https://mlsanity.com/paper/2301.03766/) (2023)
- [Learning-based AC-OPF Solvers on Realistic Network and Realistic Loads](https://mlsanity.com/paper/2205.09452/) (2022)
- [Analytical Verification of Performance of Deep Neural Network Based Time-Synchronized Distribution System State Estimation](https://mlsanity.com/paper/2311.06973/) (2023)
- [Sliced-Wasserstein-based Anomaly Detection and Open Dataset for Localized Critical Peak Rebates](https://mlsanity.com/paper/2410.21712/) (2024)
- [Adversarial Attacks and Defense Methods for Power Quality Recognition](https://mlsanity.com/paper/2202.07421/) (2022)
- [Can multivariate Granger causality detect directed connectivity of a multistable and dynamic biological decision network model?](https://mlsanity.com/paper/2408.01528/) (2024)
- [Sliced-Wasserstein Distance-based Data Selection](https://mlsanity.com/paper/2504.12918/) (2025)
- [On the Definition of Robustness and Resilience of AI Agents for Real-time Congestion Management](https://mlsanity.com/paper/2504.13314/) (2025)
- [On the Extreme Variance of Certified Local Robustness Across Model Seeds](https://mlsanity.com/paper/2601.13303/) (2026)
- [Convex training of Lipschitz-regularized shallow neural networks](https://mlsanity.com/paper/2606.19652/) (2026)
- [Finite-Sample Probabilistic Safety Certification for AI-Based Grid-Edge Coordination](https://mlsanity.com/paper/2609.28182/) (2026)

## Abstract (arXiv)

This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black-box; this has presented a major barrier for their adoption in practice. Developing a rigorous framework based on mixed integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe, and are able to systematically identify adversarial examples. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems. This paper presents the framework, methods to assess and improve neural network robustness in power systems, and addresses concerns related to scalability and accuracy. We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162-bus systems, treating both N-1 security and small-signal stability.