arXiv:2510.23196v3 Announce Type: replace Abstract: The AC Optimal Power Flow (AC-OPF) problem is central to power system operations but remains computationally challenging to solve due to its non-convex, nonlinear nature. Neural networks (NNs) offer rapid surrogates; however, their black-box behavior introduces severe risk of operational constraint violations that compromise grid safety. This paper introduces a verification-informed NN training framework that embeds global worst-case violations directly into the training objective, allowing to train models with rigorous safety guarantees. We evaluate our method across two established NN architectures for AC-OPF predictions, benchmarking both their performance and safety margins. Through rigorous post-hoc verification, we achieve substantial reductions in worst-case violations and, for the first time, successfully verify all operational constraints of large-scale AC-OPF proxies. Experiments on systems ranging from 57 to 793 buses demonstrate scalability, speed, and reliability, bridging the gap between machine learning (ML) acceleration and verified, real-time deployment of AC-OPF solutions, paving the way toward safe data-driven optimal control.