  Simulation based inference has seen increasing interest in the past few years
as a promising approach to model the non linear scales of galaxy clustering.
  The common approach using Gaussian process is to train an emulator over the
cosmological and galaxy-halo connection parameters independently for every
scales. We present a new Gaussian process model allowing to extend the input
parameter space dimensions and to use non-diagonal noise covariance matrix.
  We use our new framework to emulate simultaneously every scales of the
non-linear clustering of galaxies in redshift space from the AbacusSummit
N-body simulations at redshift $z=0.2$. The model includes nine cosmological
parameters, five halo occupation distribution (HOD) parameters and one scale
dimension. Accounting for the limited resolution of the simulations, we train
our emulator on scales from $0.3~h^{-1}\mathrm{Mpc}$ to $60~h^{-1}\mathrm{Mpc}$
and compare its performance with the standard approach of building one
independent emulator for each scales. The new model yields more accurate and
precise constraints on cosmological parameters compared to the standard
approach.
  As the new model is able to interpolate over the scales space, we are also
able to account for the Alcock-Paczynski distortion effect leading more
accurate constraints on the cosmological parameters.
