If I had to guess they are running the WRF model [1][2]. The AI part is post-processing the model output. With a fair amount of reading the manual anybody can run their own WRF. WRF scales from running on a laptop to supercomputers with 1000s of cores.
[1] https://www.mmm.ucar.edu/models/wrf [2] https://github.com/wrf-model/WRF