A new study explores the large-scale distribution of galaxies through Interpretable Machine Learning

·       Using innovative techniques to make Artificial Intelligence more transparent, this study published in Physical Review Letters unveils how neural networks learn from the large-scale distribution of galaxies—demystifying a process that was once considered a "black box."

·       The work is led by the Institute for Theoretical Physics (IFT) UAM-CSIC and the University of Chile.

Modern cosmology faces several fundamental challenges, such as understanding the nature of dark matter and dark energy, the large-scale structure of the Universe, and probing the early moments of cosmic evolution. This is linked to determining which theoretical model most accurately describes the evolution of the Universe. In a new study, published in the prestigious journal Physical Review Letters, a team of physicists has introduced a key innovation in the application of machine learning to cosmology. They used interpretability techniques for machine learning, which provide insights into how neural networks make predictions.

The research, conducted by Indira Ocampo, George Alestas, and Savvas Nesseris from the Institute for Theoretical Physics (IFT) UAM-CSIC, along with Domenico Sapone from the University of Chile, shows that the use of neural networks can enhance the analysis of observational (or simulated) data to test models beyond the standard cosmological model (ΛCDM). In this particular case, to distinguish between ΛCDM and alternative modified gravity models, such as the Hu-Sawicki f(R) model. More importantly, through the use of interpretable ML tools, they were able to see what the neural network is learning from the data, shedding light on why it was able to classify correctly between the two models. This interpretability aspect is crucial in gaining insights into the underlying mechanisms driving the classification process, but also to understand the physics behind “more important regions of data”.

Beyond the Standard Model

The ΛCDM (Lambda Cold Dark Matter) model has been the dominant reference for explaining the evolution of the Universe. This model successfully describes the accelerated expansion of the Universe, the formation of large-scale structures, and the properties of the cosmic microwave background radiation. However, it presents some discrepancies with recent observations, such as the determination of the Hubble constant, which describes the rate of expansion of the Universe, and anomalies in the distribution of matter on large scales, particularly irregularities observed in how matter is distributed across the Universe, especially at vast distances. An alternative that is under exploration to solve these discrepancies is studying beyond ΛCDM models.

The ΛCDM model is the standard in cosmology, explaining the accelerated expansion of the Universe through dark energy (represented by the cosmological constant Λ) and cold dark matter (CDM). On the other hand, an interesting alternative class of models are the so-called f(R) models, which modify Einstein’s theory of general relativity, the foundation of our understanding of gravity. At smaller scales that are within human reach (for example the Solar System), the f(R) models can recover General Relativity, but can also mimic dark energy or dark matter by altering Einstein’s equations on cosmological scales.

The Revolution of Machine Learning in Cosmology

Testing new ideas about the universe usually involves comparing predictions from different models with actual observations. Recently, machine learning (ML) has gained a lot of attention either to speed up complex calculations or to help categorize different astronomical objects, showing amazing results. However, some concerns have arisen in the scientific community because it is not always clear how these computer tools make their decisions. 

The method implemented by the researchers from the Institute for Theoretical Physics in Madrid and the University of Chile used artificial intelligence to analyze simulated data from the large-scale distribution of galaxies and successfully distinguished between the two cosmological models: ΛCDM and the f(R) model, with a very high accuracy. But more importantly, to address the challenges of transparency, they have turned to interpretable Machine Learning techniques. In particular, they used LIME (Local Interpretable Model-agnostic Explanations), a methodology that allows understanding which features of the data have a greater influence on the predictions made by the neural network. Physicists find this crucial for decision-making when validating any new theoretical approach, as Indira Ocampo, co-author of the study, explains: "Most of the methods known to date were developed due to their growing urgency in fields such as medicine, economics, and earth sciences. In cosmology, interpretability is equally important, as we rely on machine learning models to analyze vast and complex datasets, such as large-scale galaxy distributions or fluctuations in the cosmic microwave background".

A New Horizon for Computational Cosmology

The use of interpretable machine learning tools not only improves the accuracy of cosmological model selection but also lays the foundation for future applications in the exploration of the Universe. Even more crucial, are interpretability tools that can help us enhance our understanding of the fundamental physics behind the cosmological phenomena. As galaxy surveys and other astronomical observations generate increasingly large volumes of data, these techniques will be essential for extracting relevant information and advancing our understanding of the cosmos.

Ocampo, I., Alestas, G., Nesseris, S., & Sapone, D. (2025). Enhancing cosmological model selection with interpretable machine learning. Physical Review Letters, 134(4), 041002. https://doi.org/10.1103/PhysRevLett.134.041002

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