  Combining Supernovae, Baryon Acoustic Oscillations and Redshift-Space
Distortions data from the next generation of (Stage-IV) cosmological surveys,
we aim to reconstruct the expansion history up to large redshifts using
forward-modeling of $f_{\mathrm DE}(z) =
\rho_\mathrm{DE}(z)/\rho_\mathrm{DE,0}$ with Gaussian processes (GP). In order
to reconstruct cosmological quantities at high redshifts where few or no data
are available, we adopt a new approach to GP which enforces the following
minimal assumptions: a) Our cosmology corresponds to a flat
Friedman-Lema\^itre-Robertson-Walker (FLRW) universe; b) An Einstein de Sitter
(EdS) universe is obtained on large redshifts. This allows us to reconstruct
the perturbations growth history from the reconstructed background expansion
history. Assuming various DE models, we show the ability of our reconstruction
method to differentiate them from $\Lambda$CDM at $\gtrsim2\sigma$.
