So I'm guessing you mean that:
with a Neural network, you're training it to simulate a function f(x,y) and if you reach the same point, a neural network would have to give the same output, which wouldn't be correct.
Ie, f(x,y) on the first round is different from f(x,y) the second round, because you need different outputs. Or in other words, the neural network has to have the memory to know what round it is in.
FNN don't support memory.
But there are other types of neural networks, that do.
https://en.wikipedia.org/wiki/Recurrent_neural_network
The solution you're putting forward should simulate that though.
with a Neural network, you're training it to simulate a function f(x,y) and if you reach the same point, a neural network would have to give the same output, which wouldn't be correct.
Ie, f(x,y) on the first round is different from f(x,y) the second round, because you need different outputs. Or in other words, the neural network has to have the memory to know what round it is in.
FNN don't support memory.
But there are other types of neural networks, that do.
https://en.wikipedia.org/wiki/Recurrent_neural_network
The solution you're putting forward should simulate that though.