21cmEMUv3: a Hybrid Diffusion-LSTM Emulator for Joint Inference of Cosmic Dawn and Reionisation

The cosmic dawn (CD) and epoch of reionisation (EoR) mark the first billion years of cosmic history, during which the first stars and galaxies formed and drove the final major phase transition of the Universe as their radiation ionised the neutral intergalactic medium (IGM), culminating in the present-day Universe. Over the past decade, a surge of observations has begun to illuminate these periods, with upcoming observations of the redshifted 21-cm line of neutral hydrogen — a direct tracer of the neutral IGM — expected to revolutionise our understanding of the first luminous sources. Robustly interpreting these observations with Bayesian inference requires repeatedly simulating the entire Universe across high-dimensional cosmological and astrophysical parameter spaces, making ML a critical tool for tractable inference, with emulation emerging as a powerful approach. We present {\tt 21cmEMUv3}, an emulator trained on {\tt 21cmFASTv3} simulations modelling two galaxy populations, conditioned on eleven parameters ($\sigma_8$ plus ten astrophysical parameters), and designed to jointly predict seven summary observables including 21-cm power spectra, IGM thermal history, and UV luminosity functions. We emulate the 2D 21-cm PS via score-based diffusion and the remaining six summaries via long short-term memory (LSTM) networks, achieving sub-percent median accuracy across all outputs. We showcase the emulator by producing forecasts for the upcoming Square Kilometre Array (SKA), finding that SKA will enable percent-level constraints on the neutral hydrogen fraction at EoR midpoint, while further demonstrating that inference pipelines remain highly sensitive to model misspecification, an important methodological challenge for robust scientific inference with upcoming observations.