Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee

• URL: http://arxiv.org/abs/2512.11127v1
• Date: Thu, 11 Dec 2025 21:16:23 GMT
• Title: Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee
• Authors: Kshitiz Khanal,
• Abstract summary: DC-OPF problem is fundamental to power system operations, requiring rapid solutions for real-time grid management.<n>We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM)<n>Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.

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