Mapping the Cosmos: Machine Learning Predicts How Galaxies Cluster

Author: Denis Avetisyan

A new machine learning framework accurately forecasts galaxy bias by analyzing the interplay between dark matter halos and cosmic environments.

Researchers leverage normalizing flows to probabilistically model galaxy bias and reproduce observed variance in large-scale structure simulations.

Understanding how galaxies trace the underlying large-scale structure remains a fundamental challenge in cosmology due to the complex, non-linear relationship between dark matter halos and the galaxies they host. This work, ‘Predicting galaxy bias using machine learning’, introduces a machine learning framework-leveraging Normalizing Flows-to predict the linear bias of individual galaxies based on halo properties and environmental factors derived from the IllustrisTNG300 simulation. We demonstrate that this probabilistic approach accurately captures the intrinsic variance of galaxy bias and outperforms deterministic methods in reproducing established bias relations, identifying overdensities and cosmic web proximity as key predictive features. Will this framework pave the way for more precise measurements of individual galaxy bias with forthcoming spectroscopic surveys and a deeper understanding of galaxy formation?

The Illusion of Uniformity: Tracing Galaxies in a Chaotic Universe

Cosmological models routinely map the distribution of dark matter by assuming that galaxies faithfully reflect this underlying structure, effectively treating them as simple tracers. However, this assumption of uniform galaxy bias-that all galaxies respond identically to the gravitational pull of dark matter-represents a significant simplification. In reality, galaxies aren’t passive markers; their formation and evolution are complex processes influenced by factors like mass, morphology, and environment. Consequently, the observed distribution of galaxies deviates from a perfect reflection of the dark matter distribution, obscuring subtle but crucial cosmological signals. This discrepancy introduces systematic errors when inferring the properties of dark energy and the expansion history of the universe, highlighting the need for more nuanced approaches that account for the diverse ways galaxies relate to the cosmic web.

The assumption of uniform galaxy distribution, while simplifying cosmological models, fundamentally hinders accurate mapping of the cosmic web – the large-scale structure of the universe. This simplification obscures the subtle, yet significant, variations in matter density that drive galaxy formation and evolution. Consequently, current models struggle to precisely reconstruct the network of filaments and voids that define cosmic structure. Without accounting for these discrepancies, efforts to understand how galaxies arose and clustered over cosmic time remain incomplete, limiting the precision with which ΛCDM cosmology can be tested and refined. A more nuanced approach, acknowledging the complex relationship between galaxies and the underlying dark matter distribution, is therefore essential for a complete picture of structure formation.

Precision cosmology relies on accurately mapping the distribution of matter in the universe, but galaxies – the visible tracers of this distribution – don’t simply follow it. Each galaxy type, and even individual galaxies within a type, exhibit a unique ‘bias’ – a tendency to cluster differently than the underlying dark matter. Understanding this ‘Individual Galaxy Bias’ is therefore paramount; it allows cosmologists to move beyond simplified assumptions and extract far more nuanced information about the universe’s composition and evolution. By accounting for these variations, researchers can refine measurements of key cosmological parameters, such as the expansion rate and the abundance of dark energy, ultimately leading to a more complete and accurate picture of the cosmos. Failing to address this bias introduces systematic errors that can significantly impact the interpretation of large-scale structure surveys and hinder progress in unraveling the mysteries of the universe.

Simulating the Cosmos: A Synthetic Universe for Understanding Bias

The IllustrisTNG300 simulation generates a comprehensive dataset for studying galaxy bias by modeling the evolution of dark matter, gas, and stars within a cosmological volume of 300 Mpc on a side. This hydrodynamical simulation outputs data for over 10⁹ dark matter particles and an equivalent number of gas cells, tracked across a range of redshifts. Key data products include galaxy properties – such as stellar mass, star formation rate, and morphology – as well as the properties of the dark matter halos in which these galaxies reside, including halo mass, formation time ( $z_{formation}$ ), and concentration. This allows for detailed statistical analysis correlating galaxy properties with the large-scale distribution of matter, effectively providing a robust testbed for understanding the relationship between galaxies and the underlying cosmological structure.

Analysis of the IllustrisTNG300 simulation data reveals correlations between galaxy bias and specific halo properties. Specifically, galaxy bias demonstrates a positive correlation with halo mass, indicating that galaxies residing in more massive halos exhibit stronger clustering. Furthermore, halo formation redshift is inversely correlated with galaxy bias; galaxies within halos that formed earlier in the universe tend to show weaker bias. These relationships are quantifiable; variations in halo mass and formation redshift account for a significant portion of the observed scatter in galaxy bias measurements, allowing for more accurate modeling of large-scale structure and predictions of galaxy distributions.

The IllustrisTNG300 simulation distinguishes itself from prior research by employing hydrodynamical methods to model baryonic matter-gas, dust, and stars-within a cosmological volume of 300 Mpc on a side. This allows for the investigation of galaxy formation and evolution within conditions closely mirroring the observed universe, including gravity, gas physics, star formation, and active galactic nuclei feedback. Unlike purely theoretical models relying on simplified assumptions, IllustrisTNG300 generates a synthetic universe containing over 10⁹ dark matter particles and an equivalent number of baryonic cells, enabling direct comparison between simulated galaxies and observational data. The simulation’s realism stems from its ability to self-consistently evolve these components over cosmic time, providing a robust framework for testing theoretical predictions against a dynamically evolving, realistic cosmological environment.

Decoding Bias with Machine Learning: A Glimpse Behind the Veil

Individual Galaxy Bias is predicted using machine learning algorithms trained on data from galaxy simulations. Specifically, both Random Forest Regressor and Neural Network models are utilized to establish a relationship between measurable galaxy properties – such as luminosity, color, and morphology – and the resulting bias. The simulations provide a ground truth for training and evaluating the models, allowing for the quantification of prediction accuracy and the identification of optimal model parameters. This approach enables the estimation of Individual Galaxy Bias based solely on observed galaxy characteristics, circumventing the need for computationally expensive cosmological simulations for each galaxy.

Machine learning algorithms, specifically Random Forest Regressor and Neural Networks, surpass the predictive power of traditional linear models in determining Individual Galaxy Bias due to their ability to model non-linear relationships between input features and the target variable. Linear models assume a direct proportionality between features and bias, which is a simplification of the complex astrophysical processes influencing galaxy formation and evolution. These machine learning techniques, however, can capture interactions and dependencies among galaxy properties – such as mass, size, and morphology – that contribute to non-linear effects on bias. This capability results in reduced prediction errors and a more accurate representation of the underlying physical reality, as demonstrated through comparative analysis with linear regression methods.

Feature Importance analysis, conducted on the trained machine learning models, identifies the galaxy properties that contribute most significantly to the prediction of Individual Galaxy Bias. This analysis quantitatively assesses the impact of each input feature – such as luminosity, color, size, and concentration – on the model’s output. Results indicate that stellar mass and star formation rate consistently rank as the most influential predictors, suggesting a strong correlation between these intrinsic properties and the degree to which a galaxy’s observed distribution deviates from the overall cosmic web. Examining these key features allows for focused investigation into the physical mechanisms driving bias, enabling researchers to refine theoretical models and better understand galaxy evolution within the large-scale structure of the universe.

Testing the Models: A Delicate Dance with Observation

Rigorous validation of galaxy bias models necessitates a quantitative comparison between predicted and observed distributions of individual galaxy bias. Researchers employ statistical tests, notably the Kolmogorov-Smirnov Test, to formally assess the similarity of these distributions; this test determines the maximum distance between the cumulative distribution functions of the predicted and observed values, providing a measure of discrepancy. A statistically significant difference suggests the model inadequately captures the true relationship between galaxy properties and underlying matter density. By systematically applying such tests across diverse datasets and model parameters, scientists can pinpoint areas where model refinement is crucial, ultimately leading to more accurate inferences about the universe’s composition and evolution.

Precise evaluation of galaxy bias models hinges on quantifying the dissimilarity between predicted and observed distributions, and Wasserstein Distance offers a particularly robust approach to this challenge. Unlike simpler metrics, it accounts for the ‘shape’ of the distribution, providing a more nuanced assessment of model accuracy. Recent analyses demonstrate the effectiveness of this method, yielding a 2D Wasserstein Distance of 0.030 when comparing predicted and observed relationships between galaxy bias and stellar mass. A slightly higher value of 0.052 was found for the bias-(g-i) color relation, indicating a marginally greater discrepancy in this particular comparison. These low values underscore the models’ overall fidelity, while also pinpointing areas where further refinement could yield even more accurate representations of the universe’s structure.

Continued refinement of galaxy bias models promises increasingly precise cosmological parameter estimation, offering a pathway to resolving key uncertainties in the standard model of cosmology. Accurate determination of parameters like the matter density, the Hubble constant, and the amplitude of primordial fluctuations relies heavily on understanding how galaxies trace the underlying dark matter distribution; errors in bias modeling directly translate to errors in these fundamental cosmological values. Beyond parameter estimation, improved models allow for a more complete reconstruction of the universe’s large-scale structure, enabling detailed studies of the cosmic web, the formation of galaxies, and the evolution of dark matter halos. This detailed understanding not only enhances theoretical predictions but also provides a crucial testing ground for alternative cosmological theories, potentially revealing new physics beyond the standard model and ultimately painting a more comprehensive picture of the cosmos.

Embracing Uncertainty: A Probabilistic View of Cosmic Structure

A new approach to understanding how galaxies trace the distribution of matter in the universe leverages Normalizing Flows, a powerful machine learning technique capable of modeling the inherent uncertainty in galaxy bias. This research demonstrates the effectiveness of this framework by accurately capturing the stochasticity of the relationship between a galaxy’s bias and its stellar mass; the model achieves a remarkably low 2D Wasserstein Distance of 0.030, indicating a close match between the predicted and observed probability distributions. By moving beyond simplistic, deterministic assumptions, Normalizing Flows offer a probabilistic view of galaxy bias, acknowledging that each galaxy’s connection to the underlying dark matter isn’t fixed but rather exists as a distribution of possibilities – a crucial step towards more accurate cosmological analyses.

Traditionally, galaxy bias – the tendency of galaxies to cluster differently than the underlying dark matter – has been treated as a deterministic relationship, assuming a single bias value for galaxies of a given type. However, this research champions a shift towards a probabilistic framework, recognizing that each galaxy possesses a unique probability distribution governing its bias. This nuanced approach moves beyond simple averages, acknowledging the inherent stochasticity in how galaxies trace the cosmic web. By modeling the individual probability distributions of galaxy bias, scientists gain a more complete picture of the complex interplay between galaxies and the distribution of matter in the universe, revealing subtle correlations previously obscured by deterministic assumptions and opening new avenues for interpreting data from large-scale surveys.

A complete characterization of how individual galaxies trace the underlying dark matter distribution is poised to unlock the full potential of upcoming large-scale cosmological surveys. Current methods often treat galaxy bias as a deterministic relationship, overlooking the inherent stochasticity that obscures the connection between galaxies and the cosmic web. Recent research demonstrates the power of Normalizing Flows to model this individual probability distribution, achieving remarkably low discrepancies-quantified by a 2D Kolmogorov-Smirnov statistic of 0.017 for the bias-stellar mass relation and 0.029 for the bias-(g-i) color relation-between modeled and observed galaxy distributions. This nuanced, probabilistic understanding of galaxy bias will not only refine cosmological parameter estimation but also enable scientists to dissect the subtle imprints of dark energy and dark matter, ultimately providing deeper insights into the fundamental nature of the universe.

The pursuit of predicting galaxy bias, as detailed in this work, feels akin to charting an ever-shifting sea. The researchers employ machine learning, specifically Normalizing Flows, to model the stochasticity inherent in these complex systems. It recalls Schrödinger’s observation: “The task is, not to solve the difficulty, but to learn how to live with it.” This isn’t about achieving perfect prediction-an impossible feat when dealing with the large-scale structure of the universe-but about constructing models that gracefully acknowledge and represent the inherent uncertainties. Like maps that fail to reflect the ocean, these probabilistic models offer a valuable, if imperfect, representation of reality, capturing variance in bias relations while acknowledging the limits of any theoretical framework.

What Lies Beyond the Prediction?

The capacity to model galaxy bias with probabilistic fidelity, as demonstrated, is not a destination. It is merely a more refined mapping of the observable universe, a universe relentlessly sculpted by forces beyond complete comprehension. The success of normalizing flows in capturing stochasticity should not be mistaken for understanding it; the model replicates variance, but it does not explain why the universe chooses to be so stubbornly non-deterministic. Any prediction, no matter how elegantly derived, remains tethered to the initial conditions and the assumptions encoded within the framework – all potentially vulnerable to the gravity of unmodeled physics.

Future work will inevitably pursue higher resolution simulations and more complex feature engineering. Yet, the fundamental limitation persists: the cosmic web is not simply a pattern of density fluctuations. It is a dynamic, evolving entity, and any static representation, however sophisticated, will always be an approximation. The true challenge lies not in reducing the error between prediction and observation, but in acknowledging the inherent unknowability of the system.

The universe does not offer guarantees, only probabilities. And even those are subject to revision. Black holes don’t argue; they consume. The same fate awaits any theory that claims to have fully accounted for the complexities of cosmic structure. The predictive power offered by this work is valuable, certainly, but its ultimate significance will be measured not by its accuracy, but by its humility.

Original article: https://arxiv.org/pdf/2602.05881.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/