Slightly on-topic:<p>We have efficiently computable state-update equations available for weather. If neural nets are actually able to outperform those in general (and not just because of some form of sampling bias), why would that be?<p>1. They're exploiting information not available in the raw inputs to those weather models. Perhaps the number of cars driving vs parked in garages on a given day, contributing some local heat and perturbing PDE solutions away from the optimum. If this is the case, there's probably a fruitful line of research in using neural nets to estimate unmeasured parameters and using those directly in the applicable physics.<p>2. They just look better, e.g. by comparing raw neural outputs to sanitized weather reports or by using a metric biased toward low prediction variance at the expense of accuracy or something (this could be as simple as grading the neural net's probability distribution against the weather model's raw predicted output too, not considering the epistemological tweaked predictions the physics model also produced, thus implicitly giving the neural net and edge because the physics model can't get partial credit, even when worthy of it's and the AI can). Those sorts of mistakes are shockingly easy to make, even with much thought and careful review. Time will tell, I hope.<p>3. The gains are in some form of auxiliary data, like cheaply extrapolating a coarse forecast into a fine-grained forecast (superresolution/hallucination), or cheaply approximating a single weather estimate without fleshing out the details of the entire grid. This is potentially incredibly valuable, at the obvious cost of occasionally being very wrong. Use such predictions with care.<p>I don't think that list is exhaustive, but I'm not holding my breath too much either. Gaining an extra day of hurricane touchdown accuracy, for example, takes immense amounts of data. We've slowly made those gains, but for a neural net to do noticeably better there would have to be major problems in our original problem formulation.<p>Slightly off-topic:<p>I'd love an easy way to get conditional probabilities in my forecasts. Some sort of raw, fine-grained data allowing those computations would be a god-send. When a forecast says there's a 30% chance of rain each hour, do they mean we're definitely getting rain and don't know which hour (like the very tall, narrow thunderstorms often traversing west->east in tornado alley), do they mean we're getting a spotty amount of rain that entire period (drizzling off and on like in southeast Alaskan summers), do they mean there's a 30% chance the storm hits us and rains continuously and a 70% chance it skirts by (it's commonly easy to predict there will be a storm but not necessarily exactly where or when with respect to communities/times on the boundaries)? Those have drastic impacts on my plans for the day, and the raw data has that nuance, but it's not obtainable from any weather report I've seen.