People have definitely tried this kind of thing, but so far -- from what I've seen -- Game of Life problems seem to be highly resistant to neural-net types of solutions.
Take spaceships, for example. You can train a neural net to recognize spaceships, but there aren't any reliably recognizable features that can distinguish a spaceship from a non-spaceship. To find out if a never-before-seen pattern is a spaceship with period N, you really have to run it for N ticks and see if you get the same pattern back again at an offset. Visual similarity with other spaceships just plain isn't relevant, unless the similarity is 100%; a pattern with a 99% match on a 100-cell spaceship will almost always be ... not a spaceship at all.
A good analogy for this might be training a neural net against images of prime numbers up to 997, printed in decimal in some standard font. Sure, you can train a neural net to recognize prime numbers less than 1000, with great accuracy ... but primality isn't a visual property of a printed number, it's something that you have to do some mathematical tests to find out about.
So if you try your trained neural net on prime numbers above 1000, you're going to be rather disappointed with its performance. CA spaceship recognition is the same kind of problem... possibly worse, since you could at least have some hope of a neural net correctly recognizing non-primes by their last digits.
Take spaceships, for example. You can train a neural net to recognize spaceships, but there aren't any reliably recognizable features that can distinguish a spaceship from a non-spaceship. To find out if a never-before-seen pattern is a spaceship with period N, you really have to run it for N ticks and see if you get the same pattern back again at an offset. Visual similarity with other spaceships just plain isn't relevant, unless the similarity is 100%; a pattern with a 99% match on a 100-cell spaceship will almost always be ... not a spaceship at all.
A good analogy for this might be training a neural net against images of prime numbers up to 997, printed in decimal in some standard font. Sure, you can train a neural net to recognize prime numbers less than 1000, with great accuracy ... but primality isn't a visual property of a printed number, it's something that you have to do some mathematical tests to find out about.
So if you try your trained neural net on prime numbers above 1000, you're going to be rather disappointed with its performance. CA spaceship recognition is the same kind of problem... possibly worse, since you could at least have some hope of a neural net correctly recognizing non-primes by their last digits.