Ly{\alpha}NNA II: Field-level inference with noisy Ly{\alpha} forest spectra

Deep learning (DL) has been shown to outperform traditional, human-defined summary statistics of the Ly{\alpha} forest in constraining key astrophysical and cosmological parameters owing to its ability to tap into the realm of non-Gaussian information. An understanding of the impact of nuisance effects such as noise on such field-level frameworks, however, still remains elusive. In this work we conduct a systematic investigation into the efficacy of DL inference from noisy Ly{\alpha} forest spectra. Building upon our previous, proof-of-concept framework (Nayak et al. 2024) for pure spectra, we constructed and trained a ResNet neural network using labeled mock data from hydrodynamical simulations with a range of noise levels to optimally compress noisy spectra into a novel summary statistic that is exclusively sensitive to the power-law temperature-density relation of the intergalactic medium. We fit a Gaussian mixture surrogate with 23 components through our labels and summaries to estimate the joint data-parameter distribution for likelihood free inference, in addition to performing inference with a Gaussian likelihood. The posterior contours in the two cases agree well with each other. We compared the precision and accuracy of our posterior constraints with a combination of two human defined summaries (the 1D power spectrum and PDF of the Ly{\alpha} transmission) that have been corrected for noise, over a wide range of continuum-to-noise ratios (CNR) in the likelihood case. We found a gain in precision in terms of posterior contour area with our pipeline over the said combination of 65% (at a CNR of 20 per 6 km/s) to 112% (at 200 per 6 km/s). While the improvement in posterior precision is not as large as in the noiseless case, these results indicate that DL still remains a powerful tool for inference even with noisy, real-world datasets.