# Input Convex Neural Networks for Optimal Voltage Regulation

arXiv: https://arxiv.org/abs/2002.08684 · HTML: https://mlsanity.com/paper/2002.08684/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 7 of 7)

- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [CDiNN -Convex Difference Neural Networks](https://mlsanity.com/paper/2103.17231/) (2021)
- [Input Convex Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.21208/) (2025)
- [Real-Time Machine-Learning-Based Optimization Using Input Convex Long Short-Term Memory Network](https://mlsanity.com/paper/2311.07202/) (2023)
- [Defining Neural Network Architecture through Polytope Structures of Dataset](https://mlsanity.com/paper/2402.02407/) (2024)
- [Optimal placement of wind farms via quantile constraint learning](https://mlsanity.com/paper/2510.01093/) (2025)

## Abstract (arXiv)

The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive power injection from inverters are calculated to maintain the voltages while satisfying power network constraints. However, existing optimization algorithms require the exact topology and line parameters of underlying distribution system, which are not known for most cases and are difficult to infer. In this paper, we propose to use specifically designed neural network to tackle the learning and optimization problem together. In the training stage, the proposed input convex neural network learns the mapping between the power injections and the voltages. In the voltage regulation stage, such trained network can find the optimal reactive power injections by design. We also provide a practical distributed algorithm by using the trained neural network. Theoretical bounds on the representation performance and learning efficiency of proposed model are also discussed. Numerical simulations on multiple test systems are conducted to illustrate the operation of the algorithm.