# Learning to Solve Network Flow Problems via Neural Decoding

arXiv: https://arxiv.org/abs/2002.04091 · HTML: https://mlsanity.com/paper/2002.04091/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

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

- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (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)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [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)
- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
- [Learning to solve Minimum Cost Multicuts efficiently using Edge-Weighted Graph Convolutional Neural Networks](https://mlsanity.com/paper/2204.01366/) (2022)
- [Reinforcement Learning for Battery Energy Storage Dispatch augmented with Model-based Optimizer](https://mlsanity.com/paper/2109.01659/) (2021)

## Abstract (arXiv)

Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example, in energy systems with high levels of uncertain renewable resources, tens of thousands of scenarios may need to be solved every few minutes. Standard iterative algorithms for linear network flow problems, even though highly efficient, becomes a bottleneck in these applications. In this work, we propose a novel learning approach to accelerate the solving process. By leveraging the rich theory and economic interpretations of LP duality, we interpret the output of the neural network as a noisy codeword, where the codebook is given by the optimization problem's KKT conditions. We propose a feedforward decoding strategy that finds the optimal set of active constraints. This design is error correcting and can offer orders of magnitude speedup compared to current state-of-the-art iterative solvers, while providing much better solutions in terms of feasibility and optimality compared to end-to-end learning approaches.