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where $h_v^{(k)}$ is node v ’s representation after k rounds of message passing, $e_{uv}$ is the edge connecting it to neighbour u , and $\psi$ and $\phi$ are learned functions — the same general operation GNoME’s crystal-graph network applies to atoms and bonds, applied here to points on a sphere and the physical processes connecting them. GraphCast predicts five surface variables and six atmospheric variables across thirty-seven pressure levels, ten days ahead, at six-hour steps [ 5 ] .

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