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Equation 9 · Part 7 · How AI for Science and Medicine Actually Works

Symbol psi

hv(k+1)=ϕ(hv(k),⨁u∈N(v)ψ(hv(k),hu(k),euv)),h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\right),
ψ\psi

What this part means

a learned function.

Its job in the formula

psi is an input to the expression that computes the quantity on the left.

Where the article explains it

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.

The passage around this formula

…update for a node v with neighbours N(v)\mathcal{N}(v) looks like hv(k+1)=ϕ(hv(k),⨁u∈N(v)ψ(hv(k),hu(k),euv))h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\right). 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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.