# DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks

arXiv: https://arxiv.org/abs/2309.12849 · HTML: https://mlsanity.com/paper/2309.12849/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 8 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 5 of 5)

- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Emulating AC OPF solvers for Obtaining Sub-second Feasible, Near-Optimal Solutions](https://mlsanity.com/paper/2012.10031/) (2020)

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

- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [Learning to Optimize by Differentiable Programming](https://mlsanity.com/paper/2601.16510/) (2026)
- [Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies](https://mlsanity.com/paper/2606.03125/) (2026)

## Abstract (arXiv)

The traditional machine learning models to solve optimal power flow (OPF) are mostly trained for a given power network and lack generalizability to today's power networks with varying topologies and growing plug-and-play distributed energy resources (DERs). In this paper, we propose DeepOPF-U, which uses one unified deep neural network (DNN) to solve alternating-current (AC) OPF problems in different power networks, including a set of power networks that is successively expanding. Specifically, we design elastic input and output layers for the vectors of given loads and OPF solutions with varying lengths in different networks. The proposed method, using a single unified DNN, can deal with different and growing numbers of buses, lines, loads, and DERs. Simulations of IEEE 57/118/300-bus test systems and a network growing from 73 to 118 buses verify the improved performance of DeepOPF-U compared to existing DNN-based solution methods.