Quantum magnets are materials with localized magnetic moments that can host unconventional behaviors. The case in point are undoped cuprates, an abundant class of magnetic insulators with particularly rich chemistry. Understanding their diverse magnetic behaviors is impossible with the knowledge of the underlying spin model. Band-structure calculations combined with spin-model simulations offer an accurate tool to unravel spin models of cuprates. Yet, such numerical studies are limited to a handful of materials or even to a single material. Here, I will report on our progress in performing respective calculations in a high-throughput fashion and discuss whether (and how) machine learning can be employed to alleviate numerical bottlenecks.