A neural network emulator for the Lyman-$\alpha$ 1D flux power spectrum

The Lyman-$\alpha$ forest offers a unique avenue for studying the distribution of matter in the high redshift universe and extracting precise constraints on the nature of dark matter, neutrino masses, and other $\Lambda$CDM extensions. However, interpreting this observable requires accurate modelling of the thermal and ionisation state of the intergalactic medium, and therefore resorting to computationally expensive hydrodynamical simulations. In this work, we build a neural network that serves as a surrogate model for rapid predictions of the one-dimensional \lya flux power spectrum ($P_{\rm 1D}$), thereby making Bayesian inference feasible for this observable. Our emulation technique is based on modelling $P_{\rm 1D}$ as a function of the slope and amplitude of the linear matter power spectrum rather than as a function of cosmological parameters. We show that our emulator achieves sub-percent precision across the full range of scales ($k_{\parallel }=0.1$ to 4Mpc$^{-1}$) and redshifts ($z=2$ to 4.5) considered, and also for three $\Lambda$CDM extensions not included in the training set: massive neutrinos, running of the spectral index, and curvature. Furthermore, we show that it performs at the 1% level for ionisation and thermal histories not present in the training set and performs at the percent level when emulating down to $k_{\parallel}$=8Mpc$^{-1}$. These results affirm the efficacy of our emulation strategy in providing accurate predictions even for cosmologies and reionisation histories that were not explicitly incorporated during the training phase, and we expect it to play a critical role in the cosmological analysis of the DESI survey.