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The Universe is vast, and figuring out how galaxies and dark matter are distributed within it is no easy task. Usually, scientists run computer simulations that "play out" the evolution of entire regions of space billions of light-years across. But such calculations demand colossal resources and time. Dark matter is invisible, yet it acts as an invisible scaffold, determining where galaxies will gather.

This new method is like a restorer who rebuilds a huge mosaic from a few surviving fragments. Instead of modeling the entire gigantic volume, researchers take small cubes of space — only about 50 megaparsecs across (that's the distance light travels in 163 million years). There are many such cubes, each with its own density: some have a bit more matter, others a bit less. After training a model on these pieces, you can then "glue" them together into a complete picture of mass distribution.

The secret is that the model accounts for how the density of each piece affects the number of galaxies within it. Then, knowing how often regions of different densities occur, you can sum all the contributions to get a global picture. It's like wanting to know the average height of people in a city, but instead of surveying everyone, you measure heights in a few neighborhoods (poor and rich, old and new) and average them properly.

This approach opens the door to studying the smallest galaxies, which were previously hard to "catch" in large simulations. And ahead lie new telescopes like Euclid and Roman, which will collect data on billions of galaxies. To make sense of it all, we'll need exactly such fast and clever methods.

Original abstract

as written by the authors arXiv:2604.17981

We present a new method for emulating the halo mass function (HMF) and other distribution functions in large effective volumes, down to low halo masses, whilst simultaneously modifying large ranges of parameters, for a fraction of the cost of traditional periodic cosmological simulations. We demonstrate the method by selecting small regions, $$V \sim (50 \,h^{-1}{\rm Mpc})^3$$, with a range of overdensities from the Quijote suite, consisting of tens of thousands of $$(1 \,h^{-1}{\rm Gpc})^3$$ $$N$$-body simulation volumes run with varying $$\Lambda$$CDM parameters. We train a differentiable emulator, conditioned on the overdensity of the region and these global parameters, to reproduce the halo mass function in these regions. We then successfully recover the global distribution of halo masses of the entire box by integrating over the overdensity distribution. Our approach uses just $$\sim\,$$0.026% of the original simulation volume, and suggests that suites of targeted `zoom' simulations, extracted from low resolution parent volumes, can be used to emulate large volume simulations at a fraction of the computational cost, whilst simultaneously pushing the dynamic range to much lower masses than can be achieved in periodic simulations. We discuss emulation of other key dark matter and baryonic distribution functions, as well as higher order statistics, with implications for the interpretation of upcoming wide field surveys on observatories such as Euclid, Roman and Rubin.