Gaussian Process (GP) for non-stationary anisotropic random field

consider a set of realizations of spatially non-stationary and anisotropic Gaussian random field. To model such a random field, one can image it as a stationary isotropic random field living in non-homogenous spatial metric.

I would image build a GP model and let the Pyro learns the non-homogenous metric from the set of realizations.

I am a newbie in Pyro and wonder your opinion whether is it possible.

Thank you,

Can you provide more details, e.g. equations for a generative model or some Pyro pseudocode? The more specific you can make your questions, the more helpful we can be.

You might be interested in the Deep Kernel Learning example, which learns the parameters of a neural network parametrizing the kernel of a variational GP. Here is a GPyTorch example that does something similar with an exact GP.