DeepCHART: Mapping the 3D dark matter density field from Ly$\alpha$ forest surveys using deep learning

We present DeepCHART (Deep learning for Cosmological Heterogeneity and Astrophysical Reconstruction via Tomography), a deep learning framework designed to reconstruct the three-dimensional dark matter density field at redshift $z=2.5$ from Ly$\alpha$ forest spectra. Leveraging a 3D variational autoencoder with a U-Net architecture, DeepCHART performs fast, likelihood-free inference, accurately capturing the non-linear gravitational dynamics and baryonic processes embedded in cosmological hydrodynamical simulations. When applied to joint datasets combining Ly$\alpha$ forest absorption and coeval galaxy positions, the reconstruction quality improves further. For current surveys, such as Subaru/PFS, CLAMATO, and LATIS, with an average transverse sightline spacing of $d_\perp=2.4h^{-1}$cMpc, DeepCHART achieves high-fidelity reconstructions over the density range $0.4<\Delta_{\rm DM}<15$, with a voxel-wise Pearson correlation coefficient of $\rho\simeq 0.77$. These reconstructions are obtained using Ly$\alpha$ forest spectra with signal-to-noise ratios as low as 2 and instrumental resolution $R=2500$, matching Subaru/PFS specifications. For future high-density surveys enabled by instruments such as ELT/MOSAIC and WST/IFS with $d_\perp\simeq 1h^{-1}\mathrm{cMpc}$, the correlation improves to $\rho\simeq 0.90$ across a wider dynamic range ($0.25<\Delta_{\rm DM}<40$). The framework reliably recovers the dark matter density PDF as well as the power spectrum, with only mild suppression at intermediate scales. In terms of cosmic web classification, DeepCHART successfully identifies 81% of voids, 75% of sheets, 63% of filaments, and 43% of nodes. We propose DeepCHART as a powerful and scalable framework for field-level cosmological inference, readily generalisable to other observables, and offering a robust, efficient means of maximising the scientific return of upcoming spectroscopic surveys.