AI Weather Forecasting: Where Learned Models Beat the Equations

Numerical weather prediction is one of the great achievements of computational science, and it works by solving the equations of fluid motion. A learned forecast model does not solve them, does not know them, and on several standard measures beats them. Both halves of that sentence are worth taking seriously.

What a physical forecast does

A numerical weather model puts the atmosphere on a grid and integrates forward in time: fluid dynamics on a rotating sphere, thermodynamics, moisture, radiation. Processes smaller than a grid cell — convection, cloud microphysics, turbulence in the boundary layer — cannot be resolved, so they are represented by parameterisation schemes, which is where most of the craft and most of the disagreement lives. Running one forecast cycle occupies a national supercomputer for a substantial fraction of an hour.

Half of the enterprise is not the forecast at all. It is data assimilation: combining millions of observations from satellites, radiosondes, aircraft and buoys with a short prior forecast to estimate the current state of the atmosphere. Because the system is chaotic, error in that initial state grows, and forecast skill at a week out is limited more by how well you knew today than by the integration. This is also why forecasts are run as ensembles: perturb the initial state, integrate many times, and read the spread as uncertainty.

The assimilation systems have a second output that matters here. Running one fixed assimilation setup over decades of archived observations produces a reanalysis: a physically consistent, gridded reconstruction of the atmosphere’s history. That reanalysis is the training set for essentially every learned weather model, which means the learned models are downstream of the physical ones in a way that is easy to lose sight of.

What a learned forecast does instead

The setup is unusually clean. Take the atmospheric state on a grid at one time, predict the state a few hours later, and apply the model to its own output repeatedly to reach longer lead times. That is autoregressive rollout, structurally the same loop that generates text one token at a time. Architectures vary — graph networks over a mesh covering the globe, operators that work in the frequency domain, transformers over patches of the grid — but the training task is the same supervised regression against the reanalysis.

The consequence people react to first is cost. A trained model produces a global forecast in well under a minute on a single accelerator, against hours of supercomputer time. Training is expensive and happens once; inference is close to free by the standards of this field.

Where they win, and on which score

On standard deterministic verification — root mean square error against the analysis, for headline variables such as geopotential height at 500 hPa and temperature near the surface, at lead times of a few days to about a week — learned models have matched and exceeded operational physical forecasts. This has been replicated by multiple groups and by the forecasting centres themselves, which is why it moved from a curiosity to operational deployment quickly: major centres now run learned forecast systems alongside their physical ones. On the ladder in the overview of this cluster, that is the top rung, and there are not many examples of it.

The reason it happened here and not elsewhere is worth naming. Weather has the ideal verification step: every forecast is checked against the real atmosphere within days, the checking is automatic, and decades of labelled history already exist in a consistent format. Almost no other science has that.

The smoothing problem is the loss function

Now the limitation, and it is not an implementation detail. Train a model to minimise squared error and the optimal prediction under uncertainty is the conditional mean of the outcome distribution. The mean of many possible atmospheres is smoother than any of them. So a model trained this way is mathematically rewarded for hedging, and the hedging compounds with each autoregressive step.

The visible symptoms follow directly:

• Fields get blurrier with lead time. The power at small spatial scales decays faster than in a real atmospheric state. A forecast field can have excellent error statistics and not look like weather.
• Extremes are damped. Predicting the mean is exactly the wrong strategy for the tail, and the tail is what most forecast users care about.
• Precipitation suffers most. Rain is intermittent and spiky. Averaging over possibilities turns a chance of heavy local rain into a certainty of light widespread drizzle, which is the wrong answer in a way the score does not punish.
• The score rewards the flaw. Squared error against a single analysis prefers the smoothed forecast. So “beats the physical model on RMSE” and “produces a more realistic atmosphere” are separate claims, and only the first has been established by that number.

Because the cause is the objective, the fix is a different objective. The subsequent generation of systems is generative rather than regressive — diffusion-style models that sample sharp, physically plausible individual states and produce an ensemble from many samples, scored with metrics designed for probabilistic forecasts rather than for a single best guess. That is the right response, and it is a good general lesson: when a model has a systematic bias, look at what the training objective was rewarding before looking at the architecture.

What they still depend on

• The initial state. A learned model forecasts from an analysis it does not produce. That analysis comes from assimilation using a physical model and the global observing system. Learned assimilation is an active research area, but as things stand the physical stack has not been replaced — one expensive stage of it has.
• The training climate. The model has learned the statistics of the reanalysis period. Asked about an atmosphere outside those statistics it is extrapolating, which is one reason weather forecasting and climate projection are different problems rather than the same problem at different lead times.
• Conservation. Nothing in the training enforces conservation of mass or energy. Physical models get this from their construction. Whether it matters depends entirely on what you are using the output for, and it is a question to ask rather than assume.
• Resolution. A model trained on a gridded reanalysis cannot resolve what that grid does not. Convective-scale phenomena still belong to high-resolution physical models, and to radar-based nowcasting, which is a separate learned-model success story with its own verification loop.