发表机构
Argonne National Laboratory; Oak Ridge National Laboratory（阿贡国家实验室; 橡树岭国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过系统缩放实验，发现物理感知的增广拉格朗日训练在ACOPF代理模型中能以更高训练成本换取显著更优的约束满足度，且其性能随规模演化的规律与MSE训练不同。
AI 中文摘要
基于学习的交流最优潮流（ACOPF）代理模型有望比经典求解器大幅提速，但其运行价值既取决于预测精度，也取决于物理可行性。诸如增广拉格朗日（AL）等物理感知目标函数以额外的每步计算成本改善了约束满足度，然而这种权衡如何随规模变化尚未被刻画。我们在MSE和AL训练下扫描模型和数据集规模，并刻画跨电网中约束违反如何随网络规模变化。两种目标均以幂律形式改善，但速率不同：MSE主要受模型容量支配，而AL在两者间平衡。在MSE下，约束违反随网络规模的增长速度约为AL下的两倍。在匹配的硬件上，AL以约一个数量级的训练时间换取了近30倍的违反减少，且内存开销可忽略。训练目标不仅决定了代理模型的落点，还决定了其质量随规模演化的方式。
英文摘要
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 $19\times$ with $2.4\times$ the training time and negligible added memory. The training objective shapes not only where a surrogate lands but how its quality evolves with scale.
