Textbook of AI

GraphCast, introduced by Lam et al. (Google DeepMind, Science 2023), is a graph neural network that produces 10-day global weather forecasts at $0.25°$ resolution (~28 km) in roughly 60 seconds on a single TPU v4, five orders of magnitude faster than the operational European Centre for Medium-Range Weather Forecasts (ECMWF) high-resolution forecast (HRES) it surpasses on the majority of variables.

The state representation tiles the Earth at $0.25°$ resolution: a $721 \times 1440$ longitude–latitude grid at 37 pressure levels for five upper-air variables (geopotential, temperature, wind components, specific humidity) plus surface variables (2 m temperature, 10 m winds, mean sea-level pressure, total precipitation). This yields ~235 million state values per timestep. GraphCast learns a residual six-hour update $\mathbf{X}_{t+6h} = \mathbf{X}_t + f_\theta(\mathbf{X}_t, \mathbf{X}_{t-6h})$ and rolls out autoregressively to produce 10-day forecasts in 40 steps.

The architecture sidesteps the lat-lon grid's polar singularities by computing on an icosahedral mesh. A regular icosahedron is recursively refined six times to produce a near-uniform multi-resolution mesh with ~40k vertices. The forward pass is encode → process → decode: an encoder GNN maps grid features to mesh nodes via spatially local message passing; a processor GNN performs 16 rounds of message passing on the multi-resolution mesh (edges connect nodes at every refinement level so information can travel from local to global in $O(\log N)$ rounds); a decoder GNN maps mesh features back to the lat-lon grid. Each message passing layer is a standard MLP residual block on edges and nodes.

Training uses ERA5 reanalysis from 1979 to 2017 as ground truth, with the loss being area-weighted mean squared error across all variables, levels and lead times, $\mathcal{L} = \sum_t \sum_{\ell} w_\ell\, \cos\phi \cdot (\hat{x}_{t,\ell} - x_{t,\ell})^2$, where $\phi$ is latitude (correcting for grid-cell area) and $w_\ell$ is a hand-set per-variable weight reflecting forecast importance. The model is trained with curriculum on lead time: first a single 6-hour step, then progressively rolled out to 12, 18, ... hours, finally fine-tuned on full 10-day rollouts to suppress error accumulation.

On 1380 verification metrics (variable × pressure level × lead time × geographic region) GraphCast outperforms ECMWF HRES on ~90% of comparisons, particularly at longer lead times where its skill advantage grows. Tropical cyclone tracking, atmospheric river prediction and extreme heat forecasts all show meaningful improvements. The model is now ingested into ECMWF's experimental ML forecast suite alongside Pangu-Weather, FourCastNet and Aurora.

GraphCast has been criticised for inheriting ERA5's biases (it cannot beat its training data on observation-poor regions) and for its lower effective resolution than the underlying grid suggests (smoothed fine-scale structure compared to dynamical models). Even so, it represents the clearest demonstration that learned weather emulators are competitive with, and often superior to, physics-based numerical weather prediction on standard scoring metrics, at a small fraction of the compute cost.