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Abstract The rapid advancement of large-scale cosmological simulations has opened new avenues for cosmological and astrophysical research. However, the increasing diversity among cosmological simulation models presents a challenge to therobustness. In this work, we develop the Model-Insensitive ESTimator (Miest), a machine that canrobustlyestimate the cosmological parameters, Ω_mandσ₈, from neural hydrogen maps of simulation models in the Cosmology and Astrophysics with MachinE Learning Simulations project—IllustrisTNG,SIMBA, Astrid, and SWIFT-Eagle. An estimator is consideredrobustif it possesses a consistent predictive power across all simulations, including those used during the training phase. We train our machine using multiple simulation models and ensure that it only extracts common features between the models while disregarding the model-specific features. This allows us to develop a novel model that is capable of accurately estimating parameters across a range of simulation models, without being biased toward any particular model. Upon the investigation of the latent space—a set of summary statistics, we find that the implementation ofrobustnessleads to the blending of latent variables across different models, demonstrating the removal of model-specific features. In comparison to a standard machine lackingrobustness, the average performance of Mieston the unseen simulations during the training phase has been improved by ∼17% for Ω_mand 38% forσ₈. By using a machine learning approach that can extractrobust, yet physical features, we hope to improve our understanding of galaxy formation and evolution in a (subgrid) model-insensitive manner, and ultimately, gain insight into the underlying physical processes responsible forrobustness. 

Sparse reconstruction algorithms aim to retrieve high-dimensional sparse signals from a limited number of measurements. A common example is LASSO or Basis Pursuit where sparsity is enforced using an `1-penalty together with a cost function ||y − Hx||_2^2. For random design matrices H, a sharp phase transition boundary separates the ‘good’ parameter region where error-free recovery of a sufficiently sparse signal is possible and a ‘bad’ regime where the recovery fails. However, theoretical analysis of phase transition boundary of the correlated variables case lags behind that of uncorrelated variables. Here we use replica trick from statistical physics to show that when an Ndimensional signal x is K-sparse and H is M × N dimensional with the covariance E[H_{ia}H_{jb}] = 1 M C_{ij}D_{ab}, with all D_{aa} = 1, the perfect recovery occurs at M ∼ ψ_K(D)K log(N/M) in the very sparse limit, where ψ_K(D) ≥ 1, indicating need for more observations for the same degree of sparsity.