VERSUS: An excursion-set-inspired void-finder for the Stage-IV era

arXiv:2605.03779 · astro-ph.CO · Submitted 2026-08-20 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "VERSUS: An excursion-set-inspired void-finder for the Stage-IV era".

Jocelyn: The paper was written by Nathan Findlay and Seshadri Nadathur from Institute of Cosmology and Gravitation, University of Portsmouth and University of Portsmouth, Burnaby Road, Portsmouth PO1 3FX, UK.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Summary: Jocelyn: Let's talk about what VERSUS actually does, because it’s quite different from standard void-finding methods.

Subrahmanyan: Traditionally, algorithms like VIDE find voids based on topology—the shape of the density field—which tends to find very large, non-spherical structures.

Vera: But this is where the theory comes in; those topological voids often don't match the predictions from the excursion set formalism, which is how we theoretically predict void sizes and abundances.

Jocelyn: VERSUS tackles this by taking a different approach, identifying spherical underdensities first using a density threshold.

Subrahmanyan: It starts with these simple spheres, then it applies a crucial step: merging overlapping spheres of different sizes.

Vera: This means the final void catalogue isn't limited to just perfect spheres; it can be naturally non-spherical and still correspond to the true physical underdensity.

Jocelyn: The whole process is designed so that the resulting catalogue matches those theoretical predictions without needing any post-processing steps, which is a first for something like this.

Subrahmanyn: It's a direct way of finding voids that respect the physics of hierarchical structure formation rather than just relying on geometric shapes.

Vera: It seems like this method truly captures the essence of what an underdense region should be, not just its outline.

Improvements: Jocelyn: Now, let's look at how VERSUS improves things further when it deals with real-world data.

Vera: It's not just about finding the voids; we have to deal with messy surveys that have irregular holes or selection functions, right?

Jocelyn: And this is where VERSUS shines because of its handling of complex survey footprints using a random catalogue.

Subrahmanyan: The ability to integrate the selection function directly into the density field calculation is a massive advantage for rigorous analysis.

Vera: It means we don't have to apply ad hoc corrections to our results, which is always a concern when comparing observation to simulation.

Jocelyn: Plus, it’ incredibly efficient; the underlying routines are written in C and Cython, making it fast enough for simulation-based modeling approaches.

Subrahmanyan: That speed is vital because we can now run much more complex simulations and then analyze them with a tool that scales well with the number of cells.

Vera: It’s not just about finding the voids; we’ are enabling a whole new class of fast, consistent cosmic void analyses for Stage-IV surveys.

Comparison and Validation: Jocelyn: The authors didn't just make claims; they rigorously validated VERSUS against two distinct types of simulations.

Subrahmanyan: They used a simple toy model to check how the algorithm handles shot noise in discrete particle fields, which is a good baseline test.

Vera: But then they moved to the big one: a high-fidelity mock from the AbacusSummit simulation, which is huge and incredibly realistic.

Jocelyn: And here VERSUS proved its worth; it achieved strong agreement with the theoretical predictions for the void size function across a wide range of sizes.

Subrahmanyan: The results show that while traditional methods like VIDE required aggressive post-processing to clean up their catalogues, VERSUS produces a self-consistent result right from the first pass.

Vera: It's fascinating to see how well it performs even in those complex scenarios where the survey footprint is irregular, as shown in Figure five.

Jocelyn: The data confirms that we can truly trust this algorithm to accurately recover void centers and radii, even when dealing with a large number of galaxies.

Conclusion: Vera: So, to wrap up this discussion on VERSUS: we have a powerful tool for finding cosmic voids that directly aligns with the core predictions of modern cosmology.

Subrahmanyan: It successfully combines the physical insight of the excursion set formalism with a robust, efficient algorithm that handles real-world survey data without needing those unphysical post-processing steps.

Jocelyn: The fact that it's modular and fast means we can now move from simple toy models to performing actual, large-scale statistical analysis on future surveys like DESI.

Vera: And the authors have even provided an analytical expression for the uncertainty in void radius estimation, which is a huge benefit for robust cosmological inference.

Subrahmanyn: It really opens up a new pathway for unifying our analytic models and simulation results when it comes to cosmic voids.

Jocelyn: It feels like we’re standing on the brink of some much more precise and consistent studies of the universe's emptiest parts.

Nathan Findlay, Seshadri Nadathur

Institute of Cosmology and Gravitation, University of Portsmouth · University of Portsmouth, Burnaby Road, Portsmouth PO1 3FX, UK

astro-ph.CO

Submitted: 2026-08-20

Updated: 2026-08-21

Comments: 13 pages, 8 figures. Published in MNRAS

Journal ref: Monthly Notices of the Royal Astronomical Society, Volume 551, Issue 2, September 2026

DOI: 10.1093/mnras/stag1425

Code: https://github.com/federicomarulli/CosmoBolognaLibhttps:

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 93/100

The gist: VERSUS, a publicly available, fast void-finding algorithm, is presented as a method "designed to identify spherical underdensities in the density field that can be accurately described by excursion

Key concepts

Excursion Set Formalism: This is a theoretical method used to predict the sizes and abundances of voids in the universe. VERSUS aims to align its findings with these predictions, which are based on this formalism.
VERSUS Algorithm: VERSUS identifies spherical underdensities first using a density threshold, then merges overlapping spheres of different sizes. This process allows it to find non-spherical voids that match theoretical predictions without needing extra cleaning steps.
Stage-IV Surveys: These are future surveys for which VERSUS is designed. The tool is efficient and scalable, allowing researchers to perform fast, consistent analyses on large datasets from these upcoming surveys.

Terminology

Accuracy — 5× in this paper · explained in 1 episode
Core — 5× in this paper · explained in 2 episodes
Abundance — 4× in this paper · explained in 1 episode
Symbolic Regression — 4× in this paper · explained in 5 episodes
Trace — 4× in this paper · explained in 2 episodes
Fidelity — 3× in this paper · explained in 2 episodes
Clustering — 2× in this paper · explained in 2 episodes
Matter Power Spectrum — 2× in this paper · explained in 2 episodes
Robustness — 2× in this paper · explained in 5 episodes
Bayesian Framework — 1× in this paper · explained in 3 episodes
CMASS South Galactic Cap — 1× in this paper
Consistency — 1× in this paper · explained in 3 episodes
Dark Energy Spectroscopic Instrument — 1× in this paper
Information Gain — 1× in this paper · explained in 2 episodes
Sparsity — 1× in this paper · explained in 4 episodes

Summary

VERSUS, a publicly available, fast void-finding algorithm, is presented as a method designed to identify spherical underdensities in the density field that can be accurately described by excursion set predictions of the void size function. This tool aims to address the challenge of defining voids for cosmological analysis, as traditional topological methods often require catalogue cleaning in post-processing because they are volume-filling.

The motivation for this work stems from the fact that cosmic voids are a unique probe of non-Gaussian information in the galaxy distribution, providing sensitivity to fundamental physics such as dark energy and modified gravity. The goal is to develop an algorithm that allows for a direct, self-consistent match to theoretical predictions without the need for post-processing.

The VERSUS algorithm operates by targeting underdense regions using a threshold on the integrated density contrast. It is designed with an initial step identifying spherical underdensities and subsequently incorporates optimal merging of overlapping spheres of different sizes, producing a final void catalogue that is not limited to only spherical structures. The code itself is described as user-friendly, modular, and readily applicable to observational survey data, with its underlying routines written in C and Cython for computational speed.

Validation of the algorithm was performed against two distinct scenarios: a synthetic distribution of particles designed to trace a known input void population, and a mock galaxy sample built from an (2 h-1 Gpc) cubed AbacusSummit simulation populated with a realistic galaxy-halo connection.

The results demonstrate excellent performance, achieving "strong agreement with theoretical predictions for the void size function across the range 25 < R [h-1 Mpc] < 61 without requiring any post-processing of the void catalogue. This represents a significant achievement, described as a first for void-finders applied to the galaxy distribution."

Furthermore, VERSUS was tested against complex real-world scenarios. The algorithm successfully accounted for the non-trivial BOSS CMASS DR12 SGC survey geometry and the redshiftdependent selection, accurately recovering the VSF by employing a catalogue of random points to characterize the survey footprint.

In conclusion, VERSUS provides a robust and efficient pathway for robust and consistent cosmic void analyses with Stage-IV surveys. Its computational efficiency allows it to enable simulation-based modelling approaches, facilitating an enhanced approach to precision cosmological applications.

Improvements for AI systems

As a diligent AI researcher, I have analyzed the VERSUS methodology. This paper provides a significant paradigm shift from traditional topological void-finding methods (like VIDE/Revolver). The core innovation is moving away from purely local density minima detection towards an integrated, hierarchical, and physics-consistent approach.

The following improvements describe how the principles of VERSUS can be applied to enhance existing AI systems in large-scale structure analysis and related machine learning frameworks.

A. Implementation of Integrated Density Thresholding (v) as a Primary Feature:

Instead of relying on local density minima (which often lead to spurious voids or require complex post-processing), the AI system will use the concept of an integrated density contrast (v). This allows the system to identify regions that are statistically underdense relative to their expected mean, aligning directly with the statistical foundations of the Excursion Set Formalism.

B. Hierarchical, Physics-Consistent Merging Module:

The AI system will incorporate a sophisticated optimal merging criterion (governed by parameters like f ol and f mg). This module allows smaller, valid underdensities to be absorbed into larger structures without artificial intervention. This solves the fundamental problem of mis-centering or underestimating true void volume, ensuring the resulting catalogue accurately reflects non-linear evolution.

C. Integration of Survey Geometry via Random Catalogs:

The AI framework will incorporate a Survey-Aware Data Augmentation Module. This allows the system to model and compensate for complex real-world observational effects—such as angular masks (e.g., BOSS SGC) and redshift-dependent selection functions n(z) —by generating and processing corresponding random catalogs, eliminating the need for ad hoc correction factors in the analysis.

D. Implementation of Fast Fourier Transform (FFT) Smoothing Kernels:

The system will utilize highly efficient, iterative convolutions employing the Spherical Top-Hat (STH) kernel via FFT. This allows for rapid identification of void candidates across multiple predefined size bins (R i), ensuring that the analysis is not limited to single-scale detection but captures the full range of scales in a computationally feasible manner.

The improved, VERSUS-inspired AI system will possess the following capabilities:

A. Direct Theoretical Alignment:

The system generates void catalogues that are self-consistent with theoretical predictions (the VSF) without requiring any external post-processing or arbitrary parameter fitting (e for instance, forcing a specific void bias b v).

B. High-Fidelity Performance on Complex Data:

It can reliably extract meaningful void statistics from both synthetic toy populations and highly realistic, complex galaxy samples (like the AbacusSummit HOD mock), accurately recovering true void positions and radii even when those voids are distorted by non-linear evolution.

C. Automated Bias Calibration:

By comparing its results to the known density profiles of dark matter (via b v), the system can automatically determine the appropriate tracer bias (b v) for both itself and other algorithms, providing a robust framework for interpreting observational data and moving beyond simplistic assumptions about tracer distribution.

D. High-Throughput Computational Efficiency:

Due to its optimized C/Cython implementation and O(N cells) scaling, the system can process massive datasets (e.g, billions of galaxies in Stage-IV surveys) with a significantly reduced computational footprint compared to traditional methods, enabling its use in large-scale simulation-based modeling and real-time analysis.

Abstract

We present VERSUS, a publicly available, fast void-finding algorithm designed to identify spherical underdensities in the density field that can be accurately described by excursion set predictions of the void size function. We validate the algorithm against both a synthetic distribution of particles designed to trace a known input void population, and mock galaxy sample built from a (2 h-1 Gpc) cubed AbacusSummit simulation populated with a realistic galaxy-halo connection, including systematic effects designed to mimic real survey data. In all cases, VERSUS demonstrates excellent performance, achieving strong agreement with theoretical predictions for the void size function across the range 25 < R,[h-1 Mpc] < 61 without requiring any post-processing of the void catalogue. The code is user-friendly, modular, and readily applicable to observational survey data. Its computational efficiency further enables the use of simulation-based modelling approaches, facilitating robust and consistent cosmic void analyses with Stage-IV surveys.