Hi @jpcvn,
Is the vector of times always (or usually) the same, or does it change randomly? Are there other parameters in your model that you modify? Does your model maybe have the form
f(t_1, t_2, ..., t_n, \mathbf{p}) = (y_1, y_2, ..., y_n)
with t_1 < t_2 < ... usually the same points, and the output is a time series, where each output y_i corresponds to the point in time t_i, but is also influenced by additional input parameters \mathbf{p} and by what happened before?
Then time is not an input in our UQ sense (it is not random), but a parameter (in the sense of the Model user manual, section 2.1.4). Have a look at @damarginal’s answer to this question, it sounds a bit similar to your description.
If this is not the case, could you tell us how exactly the randomness enters your problem? Can you maybe write your model in functional form as I did above, or describe the equations that your model solves, and tell us what kind of information goes into the model and what comes out?