← Back to article

Equation 10 · How AI for Science and Medicine Actually Works

What does this equation mean?

hv(k)h_v^{(k)}

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

hv(k)h_v^{(k)}

Symbol h_v^(k)

h_v^(k) is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Understand this part →

superscript

superscript

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.

Understand this part →

See an illustrated explanation →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

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 ] .

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to How AI for Science and Medicine Actually Works

Browse the mathematical compendium →