Looking for GPU support on Markov-chain Monte-Carlo (MCMC) in Python - Hamiltonian MCMC method

I am looking for MCMC codes with a GPU suport (like CUDA or OpenCL libraries) to make faster run chains in Python.

I run chains usually with MPI but I am interested in algorithms allowing to use GPU power.

In cosmology, in order to estimate the posterior, there is a plenty of codes that does MCMC but which ones could allow to exploit GPU power with MCMC ?

From your different advices, it seems that we could benefit from GPU with Pytorch for MCMC (but caution, I don't want to introduce deep learning for the moment). But I am open to any solutions.

Could anyone send me an example of bayesian inference with a GPU benefit in Python, I would be grateful.

UPDATE : I do investigations on Hamiltonian MCMC methods since it seems to provide a GPU support.

I don't know really how this H-MCMC handles the computation of chains, especially the acceptation or rejection of proposals while benefiting the power of a GPU card.

If someone could help me by giving some explanations and how I could use it in a cosmology context, the goal being to get posteriors on considered parameters.

A simple example on an Hamiltonian MCMC code in python and using CUDA would be great (I don't know if pytorch or PyMC3 are suitable to do MCMC computations with GPU, or maybe one has to apply them on a specific case...)

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