# Minimizing Worst-Case Violations of Neural Networks

arXiv: https://arxiv.org/abs/2212.10930 · HTML: https://mlsanity.com/paper/2212.10930/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 21 Dec 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [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)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence](https://mlsanity.com/paper/1405.0766/) (2014)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulation](https://mlsanity.com/paper/2106.15987/) (2021)
- [Lecture Notes on Optimal Power Flow (OPF)](https://mlsanity.com/paper/1811.00943/) (2018)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)

## Built on by (most cited first, 3 of 3)

- [Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow](https://mlsanity.com/paper/2405.06109/) (2024)
- [Correctness Verification of Neural Networks Approximating Differential Equations](https://mlsanity.com/paper/2402.07621/) (2024)
- [Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees](https://mlsanity.com/paper/2303.13228/) (2023)

## Abstract (arXiv)

Machine learning (ML) algorithms are remarkably good at approximating complex non-linear relationships. Most ML training processes, however, are designed to deliver ML tools with good average performance, but do not offer any guarantees about their worst-case estimation error. For safety-critical systems such as power systems, this places a major barrier for their adoption. So far, approaches could determine the worst-case violations of only trained ML algorithms. To the best of our knowledge, this is the first paper to introduce a neural network training procedure designed to achieve both a good average performance and minimum worst-case violations. Using the Optimal Power Flow (OPF) problem as a guiding application, our approach (i) introduces a framework that reduces the worst-case generation constraint violations during training, incorporating them as a differentiable optimization layer; and (ii) presents a neural network sequential learning architecture to significantly accelerate it. We demonstrate the proposed architecture on four different test systems ranging from 39 buses to 162 buses, for both AC-OPF and DC-OPF applications.