Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Scaling Laws of Machine Learning for Optimal Power Flow

Xinyi Liu, Xuan He, Yize Chen

TL;DR

The paper tackles how ML-based OPF solutions scale with data and compute, revealing predictable power-law relationships for both DCOPF and ACOPF using DNNs and PINNs. It introduces a rigorous methodology with data- and compute-focused experiments, showing rapid improvements in prediction accuracy with more data or compute, but slower gains in physical feasibility, particularly for reactive-power constraints. A key contribution is the identification of a compute-optimal frontier and the finding that feasibility can be more challenging to scale than accuracy, informing principled design of data collection and training strategies for ML-OPF deployments. Practically, these scaling laws enable principled budgeting and architecture choice to meet real-time performance requirements in power-system operations.

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.

Scaling Laws of Machine Learning for Optimal Power Flow

TL;DR

The paper tackles how ML-based OPF solutions scale with data and compute, revealing predictable power-law relationships for both DCOPF and ACOPF using DNNs and PINNs. It introduces a rigorous methodology with data- and compute-focused experiments, showing rapid improvements in prediction accuracy with more data or compute, but slower gains in physical feasibility, particularly for reactive-power constraints. A key contribution is the identification of a compute-optimal frontier and the finding that feasibility can be more challenging to scale than accuracy, informing principled design of data collection and training strategies for ML-OPF deployments. Practically, these scaling laws enable principled budgeting and architecture choice to meet real-time performance requirements in power-system operations.

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.
Paper Structure (18 sections, 8 equations, 2 figures, 4 tables)

This paper contains 18 sections, 8 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Deep Learning Testbeds
  4. Evaluation Metrics
  5. Prediction Accuracy
  6. Physical Feasibility
  7. Speed
  8. Scaling Law Discovery
  9. Scaling Law Experiments
  10. Experiment Setups
  11. Results for Data Scaling
  12. Accuracy Follows Steep Power-Law Scaling
  13. Violations Exhibit Structural Scaling Bottleneck
  14. Feasibility-Accuracy Trade-off in DL Structure
  15. Results for Compute Scaling
  16. ...and 3 more sections

Figures (2)

  • Figure 1: (First two rows) Data and (Last two rows) system scaling. Fitted power law scaling functions are also drawn.
  • Figure 2: Compute Scaling on 118-bus system. IsoLoss contours show prediction error (color) versus training compute (FLOPs) and model size (Parameters). Dashed line: efficiency frontier. (Right) Best performance per architecture (blue) and global optimum (red star); error measured as MAE for $P_g$.