Fitting a vector field with "fit" ?

I have a function that has a vector field output f(x,y) = [u, v] where u and v are matrices with size(u)=size(v) = n x n.

Instead of surface fitting with z = f(x,y), I would like to fit this function to vector field from experimental data.

Similar to the question asked in this thread: https://nl.mathworks.com/matlabcentral/answers/58763-fitting-vector-valued-functions

The answers from 2013 proposes lsqcurvefit, but can this also be done with "fit" ? Or does anyone have a suggestion to reformulate my fitting problem?

I can only find surface fitting in the documentation of the matlab "fit" tool.

Thanks in advance! If necessary I can supply example code.