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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. 

This paper presents the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline, a codebase for rapid, user-friendly, and cutting-edge machine learning (ML) inference in astrophysics and cosmology. The pipeline includes software for implementing various neural architectures, training schema, priors, and density estimators in a manner easily adaptable to any research workflow. It includes comprehensive validation metrics to assess posterior estimate coverage, enhancing the reliability of inferred results. Additionally, the pipeline is easily parallelizable, designed for efficient exploration of modeling hyperparameters. To demonstrate its capabilities, we present real applications across a range of astrophysics and cosmology problems, such as: estimating galaxy cluster masses from X-ray photometry; inferring cosmology from matter power spectra and halo point clouds; characterising progenitors in gravitational wave signals; capturing physical dust parameters from galaxy colors and luminosities; and establishing properties of semi-analytic models of galaxy formation. We also include exhaustive benchmarking and comparisons of all implemented methods as well as discussions about the challenges and pitfalls of ML inference in astronomical sciences. All code and examples are made publicly available at https://github.com/maho3/ltu-ili. 

Abstract As the next generation of large galaxy surveys come online, it is becoming increasingly important to develop and understand the machine-learning tools that analyze big astronomical data. Neural networks are powerful and capable of probing deep patterns in data, but they must be trained carefully on large and representative data sets. We present a new “hump” of the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project: CAMELS-SAM, encompassing one thousand dark-matter-only simulations of (100h⁻¹cMpc)³with different cosmological parameters (Ω_mandσ₈) and run through the Santa Cruz semi-analytic model for galaxy formation over a broad range of astrophysical parameters. As a proof of concept for the power of this vast suite of simulated galaxies in a large volume and broad parameter space, we probe the power of simple clustering summary statistics to marginalize over astrophysics and constrain cosmology using neural networks. We use the two-point correlation, count-in-cells, and void probability functions, and we probe nonlinear and linear scales across 0.68 <R<27h⁻¹cMpc. We find our neural networks can both marginalize over the uncertainties in astrophysics to constrain cosmology to 3%–8% error across various types of galaxy selections, while simultaneously learning about the SC-SAM astrophysical parameters. This work encompasses vital first steps toward creating algorithms able to marginalize over the uncertainties in our galaxy formation models and measure the underlying cosmology of our Universe. CAMELS-SAM has been publicly released alongside the rest of CAMELS, and it offers great potential to many applications of machine learning in astrophysics:https://camels-sam.readthedocs.io. 

Abstract Many different studies have shown that a wealth of cosmological information resides on small, nonlinear scales. Unfortunately, there are two challenges to overcome to utilize that information. First, we do not know the optimal estimator that will allow us to retrieve the maximum information. Second, baryonic effects impact that regime significantly and in a poorly understood manner. Ideally, we would like to use an estimator that extracts the maximum cosmological information while marginalizing over baryonic effects. In this work we show that neural networks can achieve that when considering some simple scenarios. We made use of data where the maximum amount of cosmological information is known: power spectra and 2D Gaussian density fields. We also contaminate the data with simplified baryonic effects and train neural networks to predict the value of the cosmological parameters. For this data, we show that neural networks can (1) extract the maximum available cosmological information, (2) marginalize over baryonic effects, and (3) extract cosmological information that is buried in the regime dominated by baryonic physics. We also show that neural networks learn the priors of the data they are trained on, affecting their extrapolation properties. We conclude that a promising strategy to maximize the scientific return of cosmological experiments is to train neural networks on state-of-the-art numerical simulations with different strengths and implementations of baryonic effects. 

Abstract A wealth of cosmological and astrophysical information is expected from many ongoing and upcoming large-scale surveys. It is crucial to prepare for these surveys now and develop tools that can efficiently extract most information. We present HIF low : a fast generative model of the neutral hydrogen (H i ) maps that is conditioned only on cosmology (Ω m and σ 8 ) and designed using a class of normalizing flow models, the masked autoregressive flow. HIF low is trained on the state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. HIF low has the ability to generate realistic diverse maps without explicitly incorporating the expected two-dimensional maps structure into the flow as an inductive bias. We find that HIF low is able to reproduce the CAMELS average and standard deviation H i power spectrum within a factor of ≲2, scoring a very high R 2 > 90%. By inverting the flow, HIF low provides a tractable high-dimensional likelihood for efficient parameter inference. We show that the conditional HIF low on cosmology is successfully able to marginalize over astrophysics at the field level, regardless of the stellar and AGN feedback strengths. This new tool represents a first step toward a more powerful parameter inference, maximizing the scientific return of future H i surveys, and opening a new avenue to minimize the loss of complex information due to data compression down to summary statistics. 

Abstract In a novel approach employing implicit likelihood inference (ILI), also known as likelihood-free inference, we calibrate the parameters of cosmological hydrodynamic simulations against observations, which has previously been unfeasible due to the high computational cost of these simulations. For computational efficiency, we train neural networks as emulators on ∼1000 cosmological simulations from the CAMELS project to estimate simulated observables, taking as input the cosmological and astrophysical parameters, and use these emulators as surrogates for the cosmological simulations. Using the cosmic star formation rate density (SFRD) and, separately, the stellar mass functions (SMFs) at different redshifts, we perform ILI on selected cosmological and astrophysical parameters (Ω_m,σ₈, stellar wind feedback, and kinetic black hole feedback) and obtain full six-dimensional posterior distributions. In the performance test, the ILI from the emulated SFRD (SMFs) can recover the target observables with a relative error of 0.17% (0.4%). We find that degeneracies exist between the parameters inferred from the emulated SFRD, confirmed with new full cosmological simulations. We also find that the SMFs can break the degeneracy in the SFRD, which indicates that the SMFs provide complementary constraints for the parameters. Further, we find that a parameter combination inferred from an observationally inferred SFRD reproduces the target observed SFRD very well, whereas, in the case of the SMFs, the inferred and observed SMFs show significant discrepancies that indicate potential limitations of the current galaxy formation modeling and calibration framework, and/or systematic differences and inconsistencies between observations of the SMFs. 

Abstract Uncertain feedback processes in galaxies affect the distribution of matter, currently limiting the power of weak lensing surveys. If we can identify cosmological statistics that are robust against these uncertainties, or constrain these effects by other means, then we can enhance the power of current and upcoming observations from weak lensing surveys such as DES, Euclid, the Rubin Observatory, and the Roman Space Telescope. In this work, we investigate the potential of the electron density auto-power spectrum as a robust probe of cosmology and baryonic feedback. We use a suite of (magneto-)hydrodynamic simulations from the CAMELS project and perform an idealized analysis to forecast statistical uncertainties on a limited set of cosmological and physically-motivated astrophysical parameters. We find that the electron number density auto-correlation, measurable through either kinematic Sunyaev-Zel'dovich observations or through Fast Radio Burst dispersion measures, provides tight constraints on Ω m and the mean baryon fraction in intermediate-mass halos, f̅ bar . By obtaining an empirical measure for the associated systematic uncertainties, we find these constraints to be largely robust to differences in baryonic feedback models implemented in hydrodynamic simulations. We further discuss the main caveats associated with our analysis, and point out possible directions for future work. 

Abstract We present the Cosmology and Astrophysics with Machine Learning Simulations (CAMELS) Multifield Data set (CMD), a collection of hundreds of thousands of 2D maps and 3D grids containing many different properties of cosmic gas, dark matter, and stars from more than 2000 distinct simulated universes at several cosmic times. The 2D maps and 3D grids represent cosmic regions that span ∼100 million light-years and have been generated from thousands of state-of-the-art hydrodynamic and gravity-only N -body simulations from the CAMELS project. Designed to train machine-learning models, CMD is the largest data set of its kind containing more than 70 TB of data. In this paper we describe CMD in detail and outline a few of its applications. We focus our attention on one such task, parameter inference, formulating the problems we face as a challenge to the community. We release all data and provide further technical details at https://camels-multifield-dataset.readthedocs.io .