LLMs can do weather prediction? There is no way that is true. Considering ChatGPT sometimes insists 2+2=5, I sincerely doubt it is solving PDEs used to model weather systems.
A Large Language Model is just a text predicting Transformer (and sometimes image and/or audio predicting if they're multimodal). Transformers are general sequence to sequence predictors. The only difference between this and GPT is the data it's been trained on. They're the same kind of neural network.
Think base models. LLMs are extremely good at predicting the future when applied to human languages, as this is literally their only optimization goal. Why couldn't they also be good at predicting the future when applied to other complex forecasting tasks?
Of course what can be mathematically calculated without inference is going to be. LLMs may however be able to interpret the results of these calculations better than humans or current stochastical evaluations.