# Scaling Laws of Machine Learning for Optimal Power Flow

arXiv: https://arxiv.org/abs/2601.02706 · HTML: https://mlsanity.com/paper/2601.02706/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)

## Built on by (most cited first, 1 of 1)

- [ML-OPF-Bench: Benchmarking Machine Learning for Optimal Power Flow](https://mlsanity.com/paper/2610.04307/) (2026)

## Abstract (arXiv)

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.