Scaling Laws for Physics-Aware ACOPF Surrogate Learning

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.