[Paper Review] Learning neutrino effects in Cosmology with Convolutional Neural Networks

Elena Giusarma, Mauricio Reyes Hurtado+4 more|arXiv (Cornell University)|Oct 9, 2019

Astrophysics and Cosmic Phenomena32 references11 citations

TL;DR

This paper proposes D3M, a deep learning framework using Convolutional Neural Networks to generate cosmological simulations with massive neutrinos up to 10,000× faster than traditional N-body methods. By training on standard ΛCDM simulations, D3M accurately predicts neutrino effects, reproducing the matter power spectrum within ≈6% down to k=0.7 h/Mpc, offering a computationally efficient alternative for cosmological inference.

ABSTRACT

Measuring the sum of the three active neutrino masses, $M_ν$, is one of the most important challenges in modern cosmology. Massive neutrinos imprint characteristic signatures on several cosmological observables in particular on the large-scale structure of the Universe. In order to maximize the information that can be retrieved from galaxy surveys, accurate theoretical predictions in the non-linear regime are needed. Currently, one way to achieve those predictions is by running cosmological numerical simulations. Unfortunately, producing those simulations requires high computational resources -- several hundred to thousand core-hours for each neutrino mass case. In this work, we propose a new method, based on a deep learning network, to quickly generate simulations with massive neutrinos from standard $Λ$CDM simulations without neutrinos. We computed multiple relevant statistical measures of deep-learning generated simulations, and conclude that our approach is an accurate alternative to the traditional N-body techniques. In particular the power spectrum is within $\simeq 6\%$ down to non-linear scales $k=0.7$~ m h/Mpc. Finally, our method allows us to generate massive neutrino simulations 10,000 times faster than the traditional methods.

Motivation & Objective

• To accelerate the generation of cosmological simulations with massive neutrinos, which are computationally expensive using traditional N-body methods.
• To develop a deep learning model that accurately captures the non-linear effects of massive neutrinos on large-scale structure.
• To enable high-throughput simulation generation for cosmological parameter estimation and galaxy survey forecasting.
• To validate the model's robustness across different neutrino mass values and non-linear scales.

Proposed method

• The D3M framework employs a U-Net-like architecture with contracting, bottleneck, and expansive paths to learn spatial features from ΛCDM simulations.
• The model is trained to map standard ΛCDM simulations (without neutrinos) to corresponding simulations with massive neutrinos using a dataset of cosmological N-body simulations.
• Each convolutional block uses 3×3×3 filters with ReLU activation, batch normalization, and zero padding to stabilize training and enhance feature learning.
• Skip connections between contracting and expansive paths preserve fine-scale spatial information, improving reconstruction fidelity.
• The final 1×1×1 convolution maps learned features to the 3D output simulation cube, enabling high-resolution prediction of matter density fields.
• The model is evaluated using statistical measures such as the matter power spectrum and transfer function to quantify accuracy across scales.

Experimental results

Research questions

• RQ1 Can a deep learning model accurately predict the non-linear effects of massive neutrinos on large-scale structure without running full N-body simulations?
• RQ2 How well does the D3M model reproduce the matter power spectrum across both linear and non-linear scales compared to reference N-body simulations?
• RQ3 To what extent is the D3M model robust to variations in neutrino mass, such as Mν = 0.6 eV?
• RQ4 Can the model generalize across different neutrino mass values without retraining?
• RQ5 How does the computational speed of D3M compare to traditional N-body simulation methods in generating massive neutrino simulations?

Key findings

• The D3M model reproduces the matter power spectrum within ≈6% of reference N-body simulations down to k = 0.7 h/Mpc, demonstrating high accuracy in the non-linear regime.
• For a neutrino mass of Mν = 0.6 eV, the transfer function deviates from unity by only ≈8% at k ≈ 0.5 h/Mpc, indicating strong agreement with the target simulation.
• The model achieves a 10,000× speedup in simulation generation compared to traditional N-body methods, enabling rapid high-throughput cosmological modeling.
• The D3M model shows robustness across different neutrino mass values, maintaining high accuracy even when trained on one mass and tested on another.
• The inclusion of skip connections and batch normalization significantly improves the model’s ability to preserve small-scale spatial features and stabilize training.
• The transfer function analysis confirms that D3M captures the suppression of power on small scales due to neutrino free-streaming, a key signature of massive neutrinos.