Training a neural network that can map random variables to timeseries

Hi All. I have a numerical model, which accepts the vector X ( say three real parameters), and generate two timeseries y1(t), and y2(t) as the output. Note that t is discrete and the length of both timeseries is 100. I can run the model for 1000 times for different input X and can generate 1000 output timeseries y1 and y2. How can I use conventional neural network or any other NN to train a model that can generate y1(t) and y2(t) for any input X that was not part of the training?