# Learning to Optimize Power Distribution Grids using Sensitivity-Informed Deep Neural Networks

arXiv: https://arxiv.org/abs/2007.03728 · HTML: https://mlsanity.com/paper/2007.03728/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 9 of 9)

- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems](https://mlsanity.com/paper/2203.07505/) (2022)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach](https://mlsanity.com/paper/2105.00429/) (2021)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [PowerGNN: A Topology-Aware Graph Neural Network for Electricity Grids](https://mlsanity.com/paper/2503.22721/) (2025)
- [Optimal Design of Volt/VAR Control Rules of Inverters using Deep Learning](https://mlsanity.com/paper/2211.09557/) (2022)
- [An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees](https://mlsanity.com/paper/2304.01409/) (2023)
- [Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration](https://mlsanity.com/paper/2608.25095/) (2026)

## Abstract (arXiv)

Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow (OPF), thus shifting the computational effort from real-time to offline. Nonetheless, before training this DNN, one has to solve a large number of OPFs to create a labeled dataset. Granted the latter step can still be prohibitive in time-critical applications, this work puts forth an original technique for improving the prediction accuracy of DNNs by taking into account the sensitivities of the OPF minimizers with respect to the OPF parameters. By expanding on multiparametric programming, it is shown that although inverter control problems may exhibit dual degeneracy, the required sensitivities do exist in general and can be computed readily using the output of any standard quadratic program (QP) solver. Numerical tests showcase that sensitivity-informed deep learning can enhance prediction accuracy in terms of mean square error (MSE) by 2-3 orders of magnitude at minimal computational overhead. Improvements are more significant in the small-data regime, where a DNN has to learn to optimize using a few examples. Beyond multiparametric QPs, the approach is currently being generalized to parametric (non)-convex optimization problems.