What would be the best possible way to learn the time series of a set of variables from the time series data of another set of varaiables?

Question

I actually implemented this using GRU and it is causing dimension mismatch whenever I try to train the GRU with multiple sets of X (multivariate time series input) and Y (different multivariate time series output). X and Y are co-related and I intend to find the relations between these time series informations. Can anyone direct me in the right direction here?