Is it possible for you to post some runnable code? Am missing at least X1. Would be able to give some better advice.
But in your data / guess plot, I assume you’re basically using a GP to fit that data? That data will be tricky because it’s so smooth. You’ll have to set your priors on eta and ell very carefully. There is a huge range of ell values, basically out to infinity that will give you a smooth almost linear line so it’ll really help the sampler if you can constrain that so it doesn’t have to explore that whole space. That’ll help you use NUTS.
Another thing that’ll help is that since you’re using gp.Latent with a 1D stationary covariance, Matern52, it’s possible for you to use pm.gp.HSGP approximation. You’ll have to check the docstring of it for advice setting m and c, or specifically the text around Fig.6 here.