How do you get rid of weeds growing in artificial grass?

Weeds on artificial grass almost never come up through the backing itself. They root at the edges and seams where the turf meets real soil, or in the fine dust and organic debris that settles on the surface over years, which behaves like a very thin layer of soil sitting on top of the turf. A glyphosate-based weedkiller sprayed directly onto the weed is safe for the synthetic fibres and backing, so it is the reliable fix for both.

The edges and any join in the turf are the weak point. If the perimeter was not properly sealed or membraned against the surrounding soil and lawn during installation, weeds and grass from the border can push through or creep in from the side, which is a fitting issue rather than something spraying alone permanently fixes.

The surface itself is the less obvious source. Wind carries fine dust, pollen and organic debris onto any outdoor surface, artificial grass included, and over a few years that builds up in the pile enough for airborne seed to root into it, exactly the same failure mode that lets weeds grow on top of an ageing weed membrane. Regular brushing and occasional rinsing to clear that debris out reduces how much of a seed bed builds up in the first place.

For the weeds already there, a glyphosate-based weedkiller sprayed directly onto the leaf is the practical fix: it only affects living plant tissue, so it will not damage, melt or discolour the synthetic fibres, backing or infill. What to avoid is bleach and iron sulphate, both of which are known to stain artificial turf, and any solvent-based or petroleum product, which can damage the backing. Spot-treat the weed itself rather than drenching the surrounding turf, and treat the edges as a maintenance job you will likely repeat, since new seed can always blow in from outside your boundary.