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N(v)\mathcal{N}(v)

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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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N\mathcal{N}

Symbol N

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N(v)\mathcal{N}(v)

Equation 8 · AI for Science

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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…

Meanings in this article

  • vv: the message-passing update for a node.
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