🔭 astrophysics

Mimicking the large-scale structure of the Local Universe. Synthetic pre-labelled galaxies in large-scale structures

This paper presents a novel geometrical simulator that generates synthetic, pre-labelled galaxy catalogues mimicking the statistical properties of the Local Universe's large-scale structures, providing a consistent dataset to train machine learning models and benchmark classification algorithms for identifying clusters, filaments, walls, and voids.

Original authors: M. Alcázar-Laynez, S. Duarte Puertas, S. Verley, G. Blázquez-Calero, A. Jiménez, A. Lorenzo-Gutiérrez, D. Espada, M. Argudo-Fernández, I. Pérez

Published 2026-02-18

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CC BY 4.0

Original authors: M. Alcázar-Laynez, S. Duarte Puertas, S. Verley, G. Blázquez-Calero, A. Jiménez, A. Lorenzo-Gutiérrez, D. Espada, M. Argudo-Fernández, I. Pérez

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe isn't just a random scattering of stars, but a giant, three-dimensional spiderweb. In this cosmic web, galaxies (like our Milky Way) aren't floating alone; they are glued together in specific patterns:

Clusters: Big, crowded cities where thousands of galaxies hang out together.
Filaments: Long, thin bridges connecting these cities.
Walls: Giant, flat sheets of galaxies, like the walls of a room.
Voids: Massive, empty rooms where very few galaxies exist.

The problem is, astronomers have been arguing for years about exactly where a galaxy belongs. Is a galaxy on the edge of a void part of the empty room, or is it part of the wall? Without a clear rulebook, it's hard to test if their computer programs for sorting galaxies are actually working.

Enter the "Cosmic LEGO Simulator."

This paper introduces a new tool created by a team of astronomers to solve this problem. Think of it as a video game engine that builds a fake universe, but with a superpower: every single galaxy in the fake universe comes with a pre-written label saying exactly what it is.

Here is how they built it, using some fun analogies:

1. The Blueprint: The "Bubble Foam"

Instead of trying to guess where galaxies go, the team used a mathematical trick called Voronoi Tessellation. Imagine you drop a handful of marbles into a box of honey. If you let the honey expand outward from each marble at the same speed, the honey will eventually bump into itself, creating a honeycomb pattern of bubbles.

The center of each bubble is a Void (empty space).
The walls between bubbles are the Filaments and Walls.
The corners where three or more walls meet are the Clusters.

This gives them a perfect, geometric skeleton of the universe.

2. Populating the Universe: The "Crowd Control"

Once they had the skeleton, they needed to fill it with "fake" galaxies. But they didn't just throw them in randomly. They acted like a strict party planner:

In the Clusters (The Cities): They packed the galaxies tightly, just like real clusters, and even added a "Fingers of God" effect. This is a fancy term for a glitch in how we see fast-moving galaxies in clusters (they look stretched out like fingers). The simulator mimics this optical illusion perfectly.
In the Voids (The Empty Rooms): They kept the population very sparse, just like real empty space.
On the Walls (The Sheets): They spread galaxies out evenly across the flat surfaces.

Crucially, every galaxy generated knows its address. If a galaxy is placed in a "Void," the computer knows it is a Void galaxy. There is no ambiguity.

3. The "Malmquist Bias" Filter: The "Fading Flashlight"

Real telescopes have a problem: they can't see very faint, distant objects. It's like trying to see a candle from a mile away; you only see the bright ones.
The simulator includes a "dimming filter." As the fake galaxies get farther away, the computer randomly "turns off" the faint ones, making the fake universe look exactly like what a real telescope would see. This ensures that when scientists test their sorting algorithms, they are testing them on data that looks real, not just perfect data.

Why is this a Big Deal?

Imagine you are teaching a robot to sort laundry (socks, shirts, pants).

Before this paper: You gave the robot a pile of mixed clothes and asked it to sort them. But you didn't know the right answer yourself, so you couldn't tell if the robot was doing a good job.
With this paper: You give the robot a pile of clothes where every single item has a tag saying "Sock" or "Shirt." Now, you can run the robot's sorting program, compare its result to the tags, and say, "Hey, you put 5 socks in the shirt pile! You need to fix your algorithm!"

The Result

The team generated a massive "fake universe" that looks statistically identical to our real Local Universe (based on data from the Sloan Digital Sky Survey).

The Fake Universe: Contains about 500,000 galaxies per slice.
The Mix: About 81% are in walls/filaments, 16% are in voids, and 3% are in clusters.
The Goal: This "perfectly labeled" dataset is now available for other scientists to use. They can use it to train Artificial Intelligence (AI) and Machine Learning models to sort galaxies in the real universe with much higher accuracy.

In short: They built a "training ground" for the universe's sorting algorithms, complete with a cheat sheet, so we can finally teach our computers how to map the cosmic web correctly.

1. Problem Statement

Current observational and simulated Large-Scale Structure (LSS) catalogues suffer from a critical lack of consistency in assigning galaxies to specific cosmic structures (clusters, filaments, walls, and voids).

Lack of Standardization: There is no universally accepted classification criterion. Different algorithms often yield contradictory results for the same galaxy (e.g., classifying a galaxy at a void boundary as either a void or wall galaxy).
Training Data Deficit: Machine Learning (ML) and Deep Learning (DL) models require "ground truth" data with unique, immutable labels to train effectively. Existing N-body simulations often lack explicit structural labels for individual galaxies, making it impossible to benchmark classification algorithms or train semantic segmentation models accurately.
Goal: To generate a synthetic, purely geometrical LSS simulator that produces "pre-labelled" galaxies, where every galaxy is unambiguously assigned to a specific structure based on statistical properties derived from real observational data (specifically the Sloan Digital Sky Survey, SDSS).

2. Methodology

The authors developed a geometric simulator based on 3D Voronoi tessellation, which naturally mimics the "spiderweb" morphology of the Universe.

A. Geometric Framework

Voronoi Tessellation: The simulation space is tessellated using random generator points.
- Nodes (Vertices): Represent Clusters.
- Edges: Represent Filaments.
- Surfaces (Faces): Represent Walls.
- Cells (Volumes): Represent Voids.
Population Strategy: Galaxies are generated randomly within these geometric structures, adhering to statistical distributions observed in real surveys.

B. Parameterization & Calibration (SDSS Use Case)

The simulator is calibrated using the SDSS Main Galaxy Sample ( $z \simeq 0.1$ ) and specific reference catalogues:

Voids: Calibrated using Pan et al. (2012) (Void Finder method).
Clusters: Calibrated using Tempel et al. (2017) (Galaxy groups).
Walls/Filaments: Treated as a single category due to the lack of distinct observational catalogues and indexing limitations in the scipy.spatial.Voronoi library.

Key Statistical Distributions Implemented:

Clusters:
- Galaxy Count: Follows an exponential distribution fitted to Tempel et al. (2017) data ( $P(x) \propto e^{-x/15.03}$ ).
- Radius: Correlated with galaxy count ( $R_{max} \propto n^{1/3.32}$ ).
- Fingers of God (FoG): Radial velocity dispersion is applied based on cluster density to mimic redshift-space distortions.
Walls & Filaments:
- Populated with a mean density of $\sim 0.1$ galaxies/ $h^{-1}\text{Mpc}^3$ .
- Galaxies are distributed on 2D planes (walls) or 1D lines (filaments) with a Gaussian spread perpendicular to the structure.
Voids:
- Populated to represent $\sim 15\%$ of the total galaxy count (or based on density thresholds).
- Galaxies are placed exclusively in under-dense regions using an inverted 3D histogram to avoid "polluting" dense structures.

C. Observational Biases

To ensure the mock catalogues resemble real observations, two major biases are simulated:

Malmquist Bias: Faint galaxies at large distances are randomly discarded to match the detection limits of the SDSS survey.
FoG Effect: Velocity dispersion is applied to cluster galaxies to simulate the elongation of clusters along the line of sight in redshift space.

D. Output Generation

The simulator generates a full-sky sphere ( $R = 500 \, h^{-1}\text{Mpc}$ ), which is then sliced into six sections matching the SDSS footprint (120° in Right Ascension, 90° in Declination).
Labelling: Every generated galaxy is tagged with its structural identity (Cluster, Wall/Filament, or Void) at the moment of generation, providing a perfect "ground truth."

3. Key Contributions

Novel Geometric Simulator: A Python-based tool (open source) that generates LSS mock catalogues using Voronoi tessellation, ensuring a unique, non-ambiguous classification for every galaxy.
Pre-labelled Training Data: The primary contribution is the generation of datasets where the "true" structure of every galaxy is known, specifically designed to train and benchmark ML/DL models for LSS classification.
Statistical Fidelity: The simulator reproduces the mass and volume distributions of the SDSS catalogue, including the specific ratios of galaxies in clusters vs. voids vs. walls.
Bias Simulation: It incorporates realistic observational effects (Malmquist bias, FoG), making the synthetic data suitable for testing algorithms against real-world survey limitations.

4. Results

The authors generated mock catalogues and compared them against the reference SDSS data:

Volume & Mass Distribution:
- Clusters: $\sim 3.3\%$ of total mass, occupying only $\sim 0.07\%$ of the volume.
- Walls/Filaments: $\sim 80.8\%$ of total mass, occupying $\sim 19.3\%$ of the volume.
- Voids: $\sim 15.9\%$ of total mass, occupying $\sim 80.6\%$ of the volume.
- Note: These proportions align closely with theoretical models (e.g., Aragón Calvo 2007, Cautun et al. 2014) and observational estimates.
Structural Counts (per slice):
- Clusters: $\sim 333$ clusters containing $\sim 16,400$ galaxies.
- Walls/Filaments: $\sim 15,000$ structures containing $\sim 403,000$ galaxies.
- Voids: $\sim 1,060$ voids containing $\sim 79,400$ galaxies.
Statistical Consistency:
- The distribution of galaxy counts per cluster and cluster radii matches the fitted functions from Tempel et al. (2017).
- The FoG effect (velocity dispersion) successfully replicates the correlation between cluster size and velocity dispersion found in real data.
- Void galaxy density is uniform and matches the $\sim 10-18\%$ of mean cosmic density observed in Pan et al. (2012).

5. Significance and Future Impact

Benchmarking Tool: This simulator provides a "gold standard" dataset to evaluate the consistency and accuracy of existing LSS classification algorithms (e.g., NEXUS+, DisPerSE, CLASSIC), which currently often contradict one another.
ML/DL Advancement: It solves the "labeling problem" for semantic segmentation in astronomy. Researchers can now train Convolutional Neural Networks (CNNs) to classify galaxies by structure without the ambiguity of manual labeling or conflicting algorithmic definitions.
Flexibility: The code is modular, allowing users to adjust parameters (e.g., number of voids, density thresholds) to test edge cases or simulate different cosmological scenarios.
Open Science: The source code is publicly available, facilitating community adoption for future galaxy surveys (e.g., Euclid, DESI, LSST).

In summary, this work bridges the gap between theoretical cosmology and data-driven astronomy by providing a robust, geometrically consistent, and observationally biased synthetic universe specifically designed to train the next generation of AI tools for mapping the cosmic web.