Solutions for artificial grass are a tough one to resolve to be honest, we see lots of people asking this and have been on the look out for an ideal solution. Unfortunately nothing we've seen is an ideal solution. Some companies will explain to the customer that it will involve putting pegs through the artificial grass and ask for the customer to sign a disclaimer.
The other suggestion we've seen was using weights, but we're less sure of this solution as they would need to be very heavy to hold and this means porting around heavy weights.
You can if the ground is ok use the thinner pin pegs or the green topped pegs to make less of a hole than the large ribbed pegs.