Parameter estimation from Ly$\alpha$ forest in Fourier space using Information Maximising Neural Network

We aim to present a robust parameter estimation with simulated Lya forest spectra from Sherwood-Relics simulations suite using Information Maximizing Neural Network(IMNN) to extract maximal information from Lya 1D-transmitted flux in Fourier space. We perform 1D estimations using IMNN for IGM thermal parameters $T_0$ & $\gamma$ at z=2-4 and cosmological parameters $\sigma_8$ & $n_s$ at z=3-4. We compare our results with estimates from power spectrum using posterior distribution from Markov Chain Monte Carlo(MCMC). We then check robustness of IMNN estimates against deviation in spectral noise levels,continuum uncertainties & instrumental smoothing effects. Using mock Lya forest sightlines from publicly available CAMELS project we also check the robustness of the trained IMNN on a different simulation. We also perform a 2D-parameter estimation for $T_0$ & HI photoionization rates $\Gamma_{HI}$. We obtain improved estimates of $T_0$ & $\gamma$ using IMNN over standard MCMC approach. These estimates are also more robust against SNR deviations at z=2 & 3. At z=4 the sensitivity to noise deviations is on par with MCMC estimates. The IMNN also provides $T_0$ and $\gamma$ estimates which are robust against continuum uncertainties by extracting continuum-independent small-scale information from Fourier domain. In case of $\sigma_8$ & $n_s$ 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=6km/s). At medium or low resolutions IMNN performs similar 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 $T_0$ & $\Gamma_{HI}$ we also demonstrate how to take forward this approach observationally in the future.