# Scaling Laws for Physics-Aware ACOPF Surrogate Learning

arXiv: https://arxiv.org/abs/2609.16282 · HTML: https://mlsanity.com/paper/2609.16282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 51 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 30 of 38)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation](https://mlsanity.com/paper/2008.11827/) (2020)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (2024)
- [Strong NP-hardness of AC power flows feasibility](https://mlsanity.com/paper/1512.07315/) (2015)
- [Towards Neural Scaling Laws on Graphs](https://mlsanity.com/paper/2402.02054/) (2024)
- [Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods](https://mlsanity.com/paper/2307.16830/) (2023)
- [PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flow](https://mlsanity.com/paper/2505.22825/) (2025)
- [LUMINA: Foundation Models for Topology Transferable ACOPF](https://mlsanity.com/paper/2603.04300/) (2026)
- [QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints](https://mlsanity.com/paper/2401.06820/) (2024)
- [Physics-Informed Gradient Estimation for Accelerating Deep Learning based AC-OPF](https://mlsanity.com/paper/2502.16373/) (2025)

## Abstract (arXiv)

Learning-based surrogates for AC optimal power flow (ACOPF) promise large speedups over classical solvers, but their operational value depends on physical feasibility as much as predictive accuracy. Physics-aware objectives such as the augmented Lagrangian (AL) improve constraint satisfaction at additional per-step cost, yet how this trade-off behaves with scale is uncharacterized. We sweep model and dataset sizes under MSE and AL training, and measure how violation changes with network size. Both objectives improve as power laws: MSE prediction loss depends more on model size than on data, while the AL composite of prediction loss and violation improves comparably along both axes. Violation grows markedly more slowly with network size under AL. On matched hardware and equal training samples, AL reduces violation about 19× with 2.4× the training time and negligible added memory. The training objective shapes not only where a surrogate lands but how its quality evolves with scale.