@AndreaCogliati  Thanks for sharing. I am very interested in this topic as well, and so interested in helping to find the solution to your problem.
I took the code that you posted and I found that, for my data, the predicted solution moves rapidly to zero.  I trained with a simple sine wave (black) and got the red line when I ran your prediction code…

Screen Shot 2017-02-08 at 11.48.37 AM.png1926×1338 13 KB

(this is zoomed in towards the beginning… the training data goes on for 50,000 timesteps)