Scaling Laws of Machine Learning for Optimal Power Flow

TL;DR

This paper systematically studies how data volume and model complexity affect machine learning performance in optimal power flow tasks, revealing power-law relationships that guide efficient ML deployment in power systems.

Contribution

It presents the first comprehensive scaling laws for ML-based OPF, linking data and compute resources to accuracy, feasibility, and speed, enabling predictable ML pipeline design.

Findings

Prediction error scales with data and compute resources.

Constraint violations are characterized by the scaling laws.

Identifies the compute-optimal balance for ML models in OPF.

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.