Great Pyrenees need secure physical fencing. You can add an invisible fence and GPS collars but you still need a a physical fence. The ideal fence is a 6 ft deer fence or no climb fence.
If the dog tends to dig out, there are several options available :
A hot wire placed low to the ground
Hot wire / Electric fence is also an option make sure the hot wire is visible. The
If you have existing fence and need to reinforce it, running 2 strands of hot wire are a good option.
You can also extend the height of your fence visibly with hot wire
Coyote rollers
Sport dog fence system. The sport dog fence system is an "invisible" fence that allows you to attach the signal wire to your existing fence. This is only to be used in addition to a physical fence. It is NOT a stand alone option. It is a "shock collar" and does have fallout. We recommend the range to be as high as possible to avoid the dog blowing through and to give your dog a warning before the shock at the physical fence. With dogs that have a history of escaping, you want to also set the shock intensity on the collar itself to high to discourage any attempts of breaching the fence. Often after a while, when the dog is respectful of the fence, the collar can be loosened. This will depend on your dog and is at your own discretion.