Parameter estimation from the Lyα forest in the Fourier space using an information-maximizing neural network

Aims. Our aim is to present a robust parameter estimation with simulated Lyα forest spectra from Sherwood-Relics simulations suite by using an information-maximizing neural network (IMNN) to extract maximal information from Lyα 1D-Transmitted flux in the Fourier space. Methods. We performed 1D estimations using IMNN for intergalactic medium (IGM) thermal parameters T0 and γ at za =a 2 4, and cosmological parameters I8 and ns at za =a 3 4. We compared our results with estimates from the power spectrum using the posterior distribution from a Markov chain Monte Carlo (MCMC). We then checked the robustness of IMNN estimates against deviation in spectral noise levels, continuum uncertainties, and instrumental smoothing effects. Using mock Lyα forest sightlines from the publicly available CAMELS project, we also checked the robustness of the trained IMNN on a different simulation. As a proof of concept, we demonstrated a 2D-parameter estimation for T0 and HaI photoionization rates, ÎÃ Â"HI. Results. We obtain improved estimates of T0 and γ using IMNN over the standard MCMC approach. These estimates are also more robust against signal-To-noise deviations at za =a 2 and 3. At za =a 4, the sensitivity to noise deviations is on par with MCMC estimates. The IMNN also provides T0 and γ estimates that are robust against continuum uncertainties by extracting small-scale continuum-independent information from the Fourier domain. In the cases of I8 and ns, the IMNN performs on par with MCMC but still offers a significant speed boost in estimating parameters from a new dataset. The improved estimates with IMNN are seen for high instrumental resolution (FWHM = 6 km s-1). At medium or low resolutions, the IMNN performs similarly to MCMC, suggesting an improved extraction of small-scale information with IMNN. We also find that IMNN estimates are robust against the choice of simulation. By performing a 2D-parameter estimation for T0 and ÎÃ Â"HI, we also demonstrate how to take forward this approach observationally in the future.