Scaling Laws of Machine Learning for Optimal Power Flow

2026-01-06

arXiv.org

AI Summary

This work addresses the lack of systematic understanding in existing machine learning approaches to optimal power flow (OPF) regarding the interplay between data scale and model computational demands, which has led to deployment strategies reliant on trial and error. For the first time, it establishes scaling laws for ML-based OPF across two key dimensions: dataset size (ranging from 0.1K to 40K samples) and model computational scale (measured in FLOPs). Through extensive ACOPF experiments, the study reveals that prediction error, constraint violation, and solution speed exhibit stable power-law relationships with resource investment. Crucially, it distinguishes between the distinct scaling behaviors of accuracy and feasibility, thereby characterizing a computational Pareto frontier that offers predictable, efficient, and reliable design principles for ML-OPF systems.

Technology Category

• Machine Learning: Scalability of ML Systems
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

Optimal power flow (OPF) is one of the fundamental tasks for power system operations. While machine learning (ML) approaches such as deep neural networks (DNNs) have been widely studied to enhance OPF solution speed and performance, their practical deployment faces two critical scaling questions: What is the minimum training data volume required for reliable results? How should ML models'complexity balance accuracy with real-time computational limits? Existing studies evaluate discrete scenarios without quantifying these scaling relationships, leading to trial-and-error-based ML development in real-world applications. This work presents the first systematic scaling study for ML-based OPF across two dimensions: data scale (0.1K-40K training samples) and compute scale (multiple NN architectures with varying FLOPs). Our results reveal consistent power-law relationships on both DNNs and physics-informed NNs (PINNs) between each resource dimension and three core performance metrics: prediction error (MAE), constraint violations and speed. We find that for ACOPF, the accuracy metric scales with dataset size and training compute. These scaling laws enable predictable and principled ML pipeline design for OPF. We further identify the divergence between prediction accuracy and constraint feasibility and characterize the compute-optimal frontier. This work provides quantitative guidance for ML-OPF design and deployments.

Problem

• Optimal Power Flow
• Scaling Laws
• Machine Learning
• Data Efficiency
• Computational Complexity

Innovation

• scaling laws
• optimal power flow
• machine learning
• physics-informed neural networks
• computational efficiency