Nice work, Marco! I'm glad to see emulators being built for DESI. I worked on emulators for DES.

Emulators have existed in astrophysics long before ML became part of the zeitgeist. The earliest cosmology emulator paper that I'm aware of is from 2009 here: https://arxiv.org/abs/0902.0429. IIRC the method came from fluid dynamics. It just so happens that the interpolators used under the hood (clasically it was GPs but is NNs latelys) are also popular in ML, and so the method gets lumped into the ML pile.

The key difference between emulation and typical ML is that emulation is always in an interpolation setting, whereas typically predictive ML is extrapolating in one way or another (e.g. predicting future events).

Congrats to the authors!