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Equation 16 · How AI for Science and Medicine Actually Works

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ϕ\phi

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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. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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ϕ\phi

Symbol phi

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.

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where hv(k)h_v^{(k)} is node v ’s representation after k rounds of message passing, euve_{uv} is the edge connecting it to neighbour u , and ψ\psi and ϕ\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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