How the data range in different dimension will affect Gaussian Process fitting currently, I am using a sklearn GPR with Matern kernel. My input looks like X=[x0...x5]. And some the 6 dimensions will range from 0 to 4000 while some others range from 0 to 2. The code runs well, but I am not sure whether I need to scale all dimensions to same range. I have not found clear evidence to support or not.

We should scale them.
We won't find "clear evidence" because usually, most applications are with a single feature in which case the range shouldn't matter too much as we optimise the length scale individually anyway. That said, with multiple features, it is not obvious what the distance $d(x_i, x_j)$ actually means especially when features are not normalised. In the case of unnormalised features, we might end up having a single feature dominate the others.
