  Measurements of the Ly$\alpha$ forest based on large numbers of quasar
spectra from sky surveys such as SDSS/eBOSS accurately probe the distribution
of matter on small scales and thus provide important constraints on several
ingredients of the cosmological model. A main summary statistic derived from
those measurements is the one-dimensional power spectrum, P1D, of the
Ly$\alpha$ absorption. However, model predictions for P1D rely on expensive
hydrodynamical simulations of the intergalactic medium, which was the limiting
factor in previous analyses. Datasets from upcoming surveys such as DESI will
push observational accuracy near the 1%-level and probe even smaller scales.
This observational push mandate seven more accurate simulations as well as more
careful exploration of parameter space. In this work we evaluate the robustness
and accuracy of simulations and the statistical framework used to constrain
cosmological parameters. We present a comparison between the grid-based
simulation code Nyx and SPH-based code Gadget in the context ofP1D. In
addition, we perform resolution and box-size convergence tests using Nyx code.
We use a Gaussian process emulation scheme to reduce the number of simulations
required for exploration of parameter space without sacrificing the model
accuracy. We demonstrate the ability to produce unbiased parameter constraints
in an end-to-end inference test using mock eBOSS- and DESI-like data, and we
advocate for the usage of adaptive sampling schemes as opposed to using a fixed
Latin hypercube design.
