How can I train a Neural Network to predict a time-series trajectory of a ball?

Hello,

I have asked this question here before but I believe I was too vague. Consider the attached figure. The blue data points represent the two trajectories of a ball. This is the data that I want to give to the Neural Network. How can I train a Neural Network to predict the entire trajectory of some intermediate case? For example, the red data points. Note that in this particular case, I plotted it in just 1 dimension, although it will need to be generalized to a 3 dimensional situation. Furthermore, note that the entire trajectory is going to be determined by the initial position of the ball, so if you can provide some additional clarity on how to specify the initial condition of the neural network and how it relates to the initial position of the ball that would be greatly appreciated.

Thank you so much for your help!

Best, Evan John