I would imagine this would be trained on actual historical weather data instead?

Pretty much all of the AI weather prediction models are trained on ECMWF ERA5, which is kinda like a numerical weather prediction model run to forecast at t=0. ERA5 is historical weather data, but it’s a “reanalysis” of it.

Indeed, you can imagine this as some sort of advanced physics-based interpolation of various measurements (land stations, satellite data, ...) to fill in every cell in a latitude-longitude grid. This is not only used for ERA5 (training data for the models), but also to determine the initial conditions for every grid cell which are used to roll out the forecast. So AI weather models depend greatly on the NWP/physics used in for reanalysis and initial conditions. That being said, there is also research being conducted in training models straight from the raw data (weather stations, satellite, ...), thus bypassing the "interpolation" step.

Yeah. I can’t remember names off the top of my head, but there are a few companies, and I think many researchers, working on AI “data assimilation” for this.

ECMWF has an experimental AIFS direct observational prediction model (AIFS-DOP) that has become competitive with their physics based IFS model on certain metrics just in the past year.

https://arxiv.org/html/2606.19093v1

Ah, yes, that’s one of them! Not to be confused with AIFS and AIFS Ensemble that are competitive with IFS, but start with the same DA as IFS.

I'm interested in understanding wheater prediction models because accurate wind forecasts make a big difference to my personal life (sports).

Is there a good overview to learn about the current models, which all just seem like cryptic acronyms to me? in apps like Windy etc. WRF, TRRM, IK-HRRR-3km, ECMWF-9km,...

I understand by now that small grid cells are better for local prediction and that thermic winds are mostly missing from them all.

Ask your favorite AI to give you a crash course, but to start the main models you need to know are the GFS and the ECMWF. In the US where available in high res, the HRRR is excellent, but doesn’t forecast very far out. The PWG/PWE 1km PredictWind models are also very good at picking up land based features and other more precise patterns. If you are in the US everything else is probably not super relevant.

Any advice will really depend on where you live and the dominant source of local error. These are all good options for the US and if the one main source of error is near surface winds around complex terrain then you can also look into WindNinja from the National Forrest Service.

https://ninjastorm.firelab.org/windninja/mobile/

Historical weather data is discrete. You need continuous state for weather modelling which is currently achieved through conventional reforecasts using those historical observations.

From a quick read: ECMWF and IBTrACS data - the former is model based (with measurement data crunched), the latter purely observational.

A more interesting question is...does differential equations based models like mamba/state space models perform better on this sort of physics problem than pure transformer LLMs?

Is it? I can't imagine why a language model would do well on this sort of problem at all.