Mapping the Cosmos with Galaxies: A New Era of Precision

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Author: Denis Avetisyan

A novel machine learning framework leverages the power of galaxy data to unlock accurate cosmological insights, even across different simulation types.

A cosmological model, trained on L-Galaxies and evaluated across diverse simulations including GAEA, SC-SAM, and IllustrisTNG, demonstrates diminished accuracy and extrapolation robustness-as evidenced by its deviation from true $ \Omega_{m} $ values and reflected in a lower $ \chi^{2} $ score-suggesting that even sophisticated theoretical frameworks are susceptible to limitations when confronted with the inherent uncertainties beyond the boundaries of their training data.
A cosmological model, trained on L-Galaxies and evaluated across diverse simulations including GAEA, SC-SAM, and IllustrisTNG, demonstrates diminished accuracy and extrapolation robustness-as evidenced by its deviation from true $ \Omega_{m} $ values and reflected in a lower $ \chi^{2} $ score-suggesting that even sophisticated theoretical frameworks are susceptible to limitations when confronted with the inherent uncertainties beyond the boundaries of their training data.

Graph neural networks, trained on semi-analytic models, demonstrate robust cosmological parameter inference from diverse galaxy catalogs.

Despite the increasing computational cost of full hydrodynamical simulations, accurately inferring cosmological parameters remains a central challenge in modern cosmology. This study, ‘Galaxy Phase-Space and Field-Level Cosmology: The Strength of Semi-Analytic Models’, demonstrates that a machine learning framework-specifically, a graph neural network trained on data from semi-analytic models-can robustly estimate matter density parameters with remarkable precision. Remarkably, this approach successfully extrapolates across diverse simulation types, from varying semi-analytic models to full hydrodynamical simulations, suggesting underlying universality in galaxy phase-space. Does this robustness indicate that semi-analytic models capture fundamental relationships independent of specific astrophysical prescriptions, solidifying their role in generating realistic mock catalogs for cosmological surveys?

The Illusion of Cosmic Certainty

Determining the fundamental properties of the universe – its age, composition, and ultimate fate – relies heavily on analyzing the large-scale structure of the cosmos, the intricate web of galaxies and dark matter. However, extracting these cosmological parameters from observations is an immensely challenging computational task. Accurately modeling the processes that govern galaxy formation and evolution – including gravity, hydrodynamics, star formation, and feedback from supermassive black holes – demands sophisticated simulations. These simulations must account for a vast number of particles and complex physical interactions, quickly escalating computational costs. The precision required for modern cosmological studies, aiming to constrain parameters to within a few percent, further exacerbates this challenge, pushing the limits of even the most powerful supercomputers and necessitating the development of innovative, efficient inference techniques.

The pursuit of precise cosmological parameters relies heavily on simulating the formation of large-scale structures in the universe, but full hydrodynamical simulations-which model gravity, gas dynamics, star formation, and feedback processes-present a significant computational challenge. These simulations require immense processing power and time, often taking weeks or months to model a single universe with specific parameters. The vastness of the cosmological parameter space-the range of possible values for quantities like the density of dark matter or the amplitude of primordial fluctuations-demands exploring countless such universes to accurately constrain these values. Consequently, traditional simulation methods become prohibitively slow, creating a bottleneck that limits the ability to fully leverage the wealth of data anticipated from next-generation galaxy surveys like the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST). This necessitates the development of faster, more efficient inference techniques to unlock the full potential of observational cosmology.

The promise of precision cosmology, driven by increasingly detailed maps of the universe from galaxy surveys, faces a significant hurdle: computational limitations. Extracting all possible information about dark energy, dark matter, and the early universe requires comparing theoretical predictions to observations across a vast range of cosmological parameters. However, the complex physics governing galaxy formation and evolution necessitates computationally expensive simulations to generate those predictions. This creates a bottleneck, preventing researchers from fully exploring the parameter space and potentially obscuring crucial insights hidden within current and forthcoming datasets like those from the Dark Energy Spectroscopic Instrument (DESI) and the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST). Consequently, the ability to refine cosmological models and address fundamental questions about the universe is directly constrained by the speed and efficiency of available computational tools and techniques.

The model accurately predicts cosmological parameters across diverse simulations-including both semi-analytic models and hydrodynamical simulations-as demonstrated by consistent truth-inference values and low χ² scores, with minimal performance degradation even after removing outlier samples.
The model accurately predicts cosmological parameters across diverse simulations-including both semi-analytic models and hydrodynamical simulations-as demonstrated by consistent truth-inference values and low χ² scores, with minimal performance degradation even after removing outlier samples.

Mapping the Cosmos with Neural Networks

Traditional methods of cosmological parameter estimation rely on summary statistics derived from galaxy catalogs, which can discard information and introduce biases. Graph Neural Networks (GNNs) present an alternative by directly learning a functional mapping between observed galaxy catalogs – represented as graphs where nodes are galaxies and edges define their relationships – and the underlying cosmological parameters that govern their formation and evolution. This direct mapping circumvents the need for hand-crafted summary statistics, potentially preserving more information from the data and reducing systematic errors in parameter inference. The GNN learns to encode the entire structural information of the galaxy catalog into a feature vector, which is then used to predict the cosmological parameters, such as $\Omega_m$, $\sigma_8$, and $H_0$.

Representing galaxy catalogs as graphs allows Graph Neural Networks (GNNs) to model inter-galaxy relationships as nodes connected by edges, where edge weights can reflect physical proximity or shared properties. This graph structure facilitates the capture of complex cosmological dependencies; for example, the spatial distribution of galaxies is directly influenced by the underlying dark matter distribution, which is itself a cosmological parameter. By learning directly on this graph representation, GNNs avoid the limitations of traditional methods that rely on summary statistics or smoothing techniques, enabling a more nuanced understanding of how cosmological parameters affect observable galaxy distributions. The network learns node embeddings that encode information about each galaxy and its relationships to others, ultimately allowing for inference of cosmological parameters from the graph’s overall structure and node properties.

The integration of Graph Neural Networks (GNNs) with training datasets produced by semi-analytic models, such as LGalaxies, enables a rapid and precise methodology for cosmological parameter estimation. LGalaxies simulations generate synthetic galaxy catalogs with known cosmological parameters, providing the labeled data necessary to train the GNN. This supervised learning approach allows the GNN to learn the complex, non-linear mapping between observed galaxy catalog features – including galaxy positions, velocities, and properties – and the underlying cosmological parameters like $\Omega_m$, $\sigma_8$, and $H_0$. Once trained, the GNN can then efficiently infer cosmological parameters directly from observed galaxy catalogs, significantly reducing the computational cost associated with traditional methods like Markov Chain Monte Carlo (MCMC) and offering inference speeds orders of magnitude faster.

Coverage versus credibility level across ten cosmological simulation datasets-L-Galaxies, GAEA, SC-SAM, Shark, Astrid, SIMBA, IllustrisTNG, SB28, Magneticum, and SWIFT-EAGLE-demonstrates the performance of the GNN+NF TARP test.
Coverage versus credibility level across ten cosmological simulation datasets-L-Galaxies, GAEA, SC-SAM, Shark, Astrid, SIMBA, IllustrisTNG, SB28, Magneticum, and SWIFT-EAGLE-demonstrates the performance of the GNN+NF TARP test.

Testing the Boundaries of Inference

The integration of a Moment Neural Network (MNN) with the Graph Neural Network (GNN) improves inference capabilities by directly predicting the posterior mean and standard deviation of cosmological parameters. This approach moves beyond simple point estimates, providing a full characterization of the posterior distribution and allowing for robust uncertainty quantification. The MNN is trained in conjunction with the GNN, leveraging the GNN’s graph-based feature extraction to inform the MNN’s prediction of these statistical moments. By explicitly modeling the posterior distribution, the combined GNN-MNN architecture offers a more complete and informative representation of the inferred parameters compared to traditional GNN implementations.

The Tests of Accuracy with Random Points (TARP) method was employed to validate the accuracy of the Graph Neural Network (GNN) and Moment Neural Network (MNN) inference pipeline. TARP involves generating a large set of random points within the defined parameter space and comparing the predicted posterior distributions from the GNN/MNN to the true values of those points. This comparison is performed using statistical measures to quantify the discrepancy between the predicted and actual distributions, assessing the model’s ability to accurately estimate parameters across the input space. Specifically, TARP evaluates both the bias and variance of the predictions, providing a comprehensive assessment of the model’s calibration and reliability.

The model demonstrates a Root Mean Squared Error (RMSE) of 0.07 when applied to cosmological parameter inference. This metric quantifies the average magnitude of the error between predicted and actual values, with a value of 0.07 indicating a relatively low degree of error in parameter estimation. Specifically, the RMSE was calculated across a test dataset of cosmological simulations, measuring the difference between the model’s inferred parameter values and the known ground truth values used to generate those simulations. This performance level suggests the model can accurately estimate cosmological parameters within a narrow margin of error, providing reliable results for downstream cosmological analyses.

The model achieves a coefficient of determination, $R^2$, of 0.45, which indicates a moderate level of explanatory power; however, performance remains consistent when tested against multiple simulation frameworks. This suggests that while the model does not fully explain the variance in the data, its predictive capability is robust and not specific to the characteristics of any single simulation environment. This consistent performance across different frameworks is a key strength, despite the moderate $R^2$ value, and highlights the model’s generalizability.

To ensure the reliability of inferences, a quality control step was implemented involving the $\chi^2$ statistic. Approximately 10% of generated samples were rejected if their $\chi^2$ value exceeded a threshold of 10. This removal process stabilizes performance by eliminating outliers and maintaining a consistent level of accuracy. The overall distribution of accepted samples yielded an average $\chi^2$ value of approximately 1, indicating a good fit between the model’s predictions and the underlying data.

Evaluation using RMSE, R-squared, mean relative error, reduced chi-squared, and percentage of removed samples demonstrates the performance of the GNN+MNN model across eight cosmological simulations, both on all data and samples selected by chi-squared values.
Evaluation using RMSE, R-squared, mean relative error, reduced chi-squared, and percentage of removed samples demonstrates the performance of the GNN+MNN model across eight cosmological simulations, both on all data and samples selected by chi-squared values.

A Universe of Possibilities

The CAMELS (Cosmological Ancient and Modern Large-scale structure Emulator Suite) project furnishes a comprehensive collection of hydrodynamical simulations that serve as the foundation for training and rigorously validating Graph Neural Networks (GNNs) designed for cosmological inference. These simulations aren’t merely theoretical exercises; they model the complex interplay of dark matter, gas, and star formation, creating a remarkably realistic digital universe. By exposing the GNN to this wealth of simulated data, researchers can assess its ability to accurately predict the large-scale structure of the cosmos – the distribution of galaxies and matter – from different cosmological parameters. This carefully constructed testbed allows for a quantifiable evaluation of the GNN’s performance before applying it to actual observational data, ensuring reliable and unbiased estimates of fundamental cosmological quantities, such as the density of dark matter and the expansion rate of the universe. The project’s simulations effectively bridge the gap between theoretical models and observational reality, accelerating progress in precision cosmology.

The ambitious scale of modern cosmological simulations and the demands of training Graph Neural Networks (GNNs) necessitate substantial computational resources. Institutions like the Flatiron Institute play a vital role by providing access to high-performance computing infrastructure, enabling researchers to process the enormous datasets generated by projects such as CAMELS. These simulations, which model the evolution of the universe and the formation of cosmic structures, require weeks or even months of continuous computation on powerful supercomputers. Furthermore, the GNNs, designed to infer cosmological parameters from these simulations, demand extensive training with numerous examples – a process that is equally computationally intensive. Without this dedicated support, the development and validation of these advanced techniques for precision cosmology would be significantly hampered, limiting the potential for breakthroughs in understanding the fundamental properties of the universe.

The culmination of this research lies in its potential to revolutionize how cosmological parameters – those defining the universe’s composition, age, and expansion rate – are determined. Future large-scale surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), will generate enormous datasets mapping billions of galaxies. Extracting meaningful cosmological information from this data is computationally intensive; however, this work demonstrates a pathway to drastically accelerate that process. By leveraging graph neural networks trained on realistic simulations, scientists anticipate being able to efficiently and accurately estimate cosmological parameters from future surveys, pushing the boundaries of precision cosmology and enabling deeper probes into the fundamental nature of the universe, including investigations of dark energy, dark matter, and the inflationary epoch following the Big Bang.

Evaluation of the GNN+NF model across eight cosmological simulation datasets-L-Galaxies, GAEA, SC-SAM, Shark, Astrid, SIMBA, SB28, Magneticum, and SWIFT-EAGLE-demonstrates performance metrics including RMSE, R-squared, mean relative error, and reduced chi-squared, assessed on both the full and chi-squared-selected samples.
Evaluation of the GNN+NF model across eight cosmological simulation datasets-L-Galaxies, GAEA, SC-SAM, Shark, Astrid, SIMBA, SB28, Magneticum, and SWIFT-EAGLE-demonstrates performance metrics including RMSE, R-squared, mean relative error, and reduced chi-squared, assessed on both the full and chi-squared-selected samples.

The research detailed herein presents a compelling case for the utility of machine learning, specifically graph neural networks, in cosmological parameter inference. It echoes a sentiment expressed by Igor Tamm: “The most important thing in science is to be honest.” The framework’s robustness-its ability to accurately infer parameters from diverse galaxy catalogs, even those generated by differing simulation types-highlights an intellectual honesty in its approach. The study doesn’t claim a single ‘true’ model, but rather a methodology adaptable to various datasets and theoretical underpinnings. This adaptability, stemming from training on semi-analytic models, allows for a cautious interpretation of observables, acknowledging the inherent uncertainties in any theoretical construct-a crucial point given the potential for models to vanish beyond the event horizon of observational limitations.

What Lies Beyond the Horizon?

The demonstrated efficacy of graph neural networks, trained upon the scaffolding of semi-analytic models, offers a compelling, if temporary, victory. It is tempting to believe a model, however complex, can truly encapsulate the underlying physics governing galaxy formation. Yet, the success of inferring cosmological parameters across diverse simulation types hints not at a final truth, but at a particularly adept form of mimicry. Any simplification inherent in semi-analytic models, or indeed any modeling approach, requires strict mathematical formalization to delineate the boundaries of its validity – boundaries which, one suspects, are perpetually receding.

The application of normalizing flows to map between different simulation outputs represents a clever navigational tool, but it does not alter the fundamental challenge: the inherent limitations of our observational window. Future work must confront the question of systematic uncertainties – not merely refining parameter inference, but rigorously quantifying the model dependence of the results. The strength of this framework lies in its robustness, but robustness should not be mistaken for reality.

Ultimately, the pursuit of cosmological parameters is a dance with incompleteness. Each parameter estimated, each model refined, is merely a temporary foothold against the inevitable erosion of knowledge. The horizon of understanding, like that of a black hole, promises to consume any claim of absolute certainty.

Original article: https://arxiv.org/pdf/2512.10222.pdf

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

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2025-12-12 20:10