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Equation 9 · Part 13 · How AI for Science and Medicine Actually Works

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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),
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

GraphCast , described by Remi Lam and colleagues at Google DeepMind in a 2023 paper published in Science, replaces the equation-integration step with a trained graph neural network operating on an encoder–processor–decoder structure. Weather variables at roughly one million points on a 0.25-degree global grid are first encoded onto a spherical mesh; a processor network then updates each mesh node’s representation by passing messages between it and its neighbours, repeated across the mesh’s structure so that information can propagate across the globe within a single forward pass; a decoder then reads the updated mesh back out to the original grid to produce the forecast. In general form, a…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the surrounding passage

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