# DeepOPF: Deep Neural Network for DC Optimal Power Flow

arXiv: https://arxiv.org/abs/1905.04479 · HTML: https://mlsanity.com/paper/1905.04479/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2019.

## Built on by (most cited first, 30 of 32)

- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [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)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (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)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach](https://mlsanity.com/paper/2105.00429/) (2021)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach](https://mlsanity.com/paper/2110.01653/) (2021)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making](https://mlsanity.com/paper/2311.06972/) (2023)
- [Minimizing Worst-Case Violations of Neural Networks](https://mlsanity.com/paper/2212.10930/) (2022)
- [PowerGNN: A Topology-Aware Graph Neural Network for Electricity Grids](https://mlsanity.com/paper/2503.22721/) (2025)
- [Flow-Aware GNN for Transmission Network Reconfiguration via Substation Breaker Optimization](https://mlsanity.com/paper/2508.01951/) (2025)
- [Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification](https://mlsanity.com/paper/2101.09306/) (2021)
- [Deep Reinforcement Learning for Optimal Power Flow with Renewables Using Graph Information](https://mlsanity.com/paper/2112.11461/) (2021)
- [Sampling Strategies for Static Powergrid Models](https://mlsanity.com/paper/2204.09053/) (2022)
- [Towards Practical Physics-Informed ML Design and Evaluation for Power Grid](https://mlsanity.com/paper/2205.03673/) (2022)
- [Machine Learning for Electricity Market Clearing](https://mlsanity.com/paper/2205.11641/) (2022)
- [DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with Multiple Load-Solution Mappings](https://mlsanity.com/paper/2206.03365/) (2022)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees](https://mlsanity.com/paper/2304.01409/) (2023)
- [Scaling Laws of Machine Learning for Optimal Power Flow](https://mlsanity.com/paper/2601.02706/) (2026)
- [Load Encoding for Learning AC-OPF](https://mlsanity.com/paper/2101.03973/) (2021)
- [Towards Understanding the Unreasonable Effectiveness of Learning AC-OPF Solutions](https://mlsanity.com/paper/2111.11168/) (2021)
- [Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees](https://mlsanity.com/paper/2303.13228/) (2023)

## Abstract (arXiv)

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving direct current optimal power flow (DC-OPF) problems. DeepOPF is inspired by the observation that solving DC-OPF for a given power network is equivalent to characterizing a high-dimensional mapping between the load inputs and the dispatch and transmission decisions. We construct and train a DNN model to learn such mapping, then we apply it to obtain optimized operating decisions upon arbitrary load inputs. We adopt uniform sampling to address the over-fitting problem common in generic DNN approaches. We leverage on a useful structure in DC-OPF to significantly reduce the mapping dimension, subsequently cutting down the size of our DNN model and the amount of training data/time needed. We also design a post-processing procedure to ensure the feasibility of the obtained solution. Simulation results of IEEE test cases show that DeepOPF always generates feasible solutions with negligible optimality loss, while speeding up the computing time by two orders of magnitude as compared to conventional approaches implemented in a state-of-the-art solver.