Calibrating Cosmological Simulations with Implicit Likelihood Inference Using Galaxy Growth Observables

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 , σ 8, 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.

Cosmology with Multiple Galaxies

“…We emphasize that this does not mean that the model uses information from individual galaxies and somehow stacks the results. Even using this subset of variables, one can construct noisy estimates of properties, like the stellar mass function, expected to be affected by cosmology (Jo et al 2023). Therefore, the source of information may arise from both individual galaxies and collective properties.…”

“…However, by using multiple galaxies, it should also be possible to infer the value of cosmological and astrophysical parameters by characterizing the impact on galaxy statistics like the stellar mass function. Recently, Busillo et al (2023) have shown that galaxy scaling relations are sensitive to both cosmology and astrophysics and derived constraints on those from real data (see also Jo et al 2023 for the impact on the star formation rate history and the stellar mass function). In this work, we thus ask ourselves how well we can infer cosmological parameters if we only have a few galaxies.…”

Constraining Cosmology with Machine Learning and Galaxy Clustering: The CAMELS-SAM Suite

“…However, full hydrodynamic simulations are computationally expensive to run, often limited to either small volumes or low resolution. This makes it difficult to thoroughly explore the parameter space of the subgrid recipes (though even CAMELS is helping to address this in Jo et al 2023).…”

“…For a neural network to learn a posterior, it requires a loss function to measure its performance (i.e., calculate the gradients it uses to update the weights between neurons in order to eventually converge on values closest to the true ones). We perform both parameter regression with a standard mean-squared error (MSE) validation criterion, and likelihood-free inference (LFI) with the method from Jeffrey & Wandelt (2020), updated for CAMELS in Villaescusa-Navarro et al (2022a) and featured in Jo et al (2023). Our parameter regression is a fast and straightforward way to measure the mean of the posterior and therefore roughly approximate the network's accuracy, while the latter trains for longer in order to also measure the posterior's standard deviation.…”

“…Machine learning enables the study of the galaxy-halo connection using nearly any type of galaxy property or feature, in particular those for which relationships are very hard to formulate or model (e.g., Jo et al 2023;Shao et al 2023c;Delgado et al 2023;Rodrigues et al 2023). Machine learning also avoids some of the limitations of "classical" methods, and it notably has the ability to find constraints with fewer samples or over a larger parameter space than a Fisher formalism or a covariance matrix use de Santi & Abramo 2022) as well as for summary statistics for which theoretical descriptions and likelihoods do not exist (Makinen et al 2021).…”