[Paper Review] Towards reconstructing the halo clustering and halo mass function of N-body simulations using neural ratio estimation

Androniki Dimitriou, Christoph Weniger+1 more|arXiv (Cornell University)|Jun 22, 2022

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper proposes a neural ratio estimation approach to reconstruct halo clustering and mass function from N-body simulation images by directly comparing simulated density maps with an analytical halo model. Using marginal neural ratio estimation, the method successfully recovers physical parameters, including the minimum halo mass cutoff, and generates realistic mock images, demonstrating a promising path toward automated, differentiable cosmological simulation analysis with deep learning.

ABSTRACT

High-resolution cosmological N-body simulations are excellent tools for modelling the formation and clustering of dark matter haloes. These simulations suggest complex physical theories of halo formation governed by a set of effective physical parameters. Our goal is to extract these parameters and their uncertainties in a Bayesian context. We make a step towards automatising this process by directly comparing dark matter density projection maps extracted from cosmological simulations, with density projections generated from an analytical halo model. The model is based on a toy implementation of two body correlation functions. To accomplish this we use marginal neural ratio estimation, an algorithm for simulation-based inference that allows marginal posteriors to be estimated by approximating marginal likelihood-to-evidence ratios with a neural network. In this case, we train a neural network with mock images to identify the correct values of the physical parameters that produced a given image. Using the trained neural network on cosmological N-body simulation images we are able to reconstruct the halo mass function, to generate mock images similar to the N-body simulation images and to identify the lowest mass of the haloes of those images, provided that they have the same clustering with our training data. Our results indicate that this is a promising approach in the path towards developing cosmological simulations assisted by neural networks.

Motivation & Objective

• To automate the inference of halo formation parameters from cosmological N-body simulations using machine learning.
• To address the challenge of high-dimensional, intractable likelihoods in simulation-based inference for cosmological structure formation.
• To reconstruct the halo mass function and clustering properties directly from dark matter density projection maps.
• To develop a differentiable, end-to-end framework that bypasses traditional likelihood computation in cosmological simulations.

Proposed method

• Employs marginal neural ratio estimation (MNRE) to approximate posterior distributions over physical parameters without explicit likelihoods.
• Trains a neural network on synthetic images generated from an analytical toy halo model with tunable parameters including halo mass function cutoff and clustering amplitude.
• Uses a two-body correlation function model to simulate halo clustering, assuming Gaussian random fields with power-law power spectra.
• Calibrates the model directly on dark-matter-only N-body simulation data (EAGLE) by matching image statistics.
• Applies data augmentation via image rotations to improve robustness and generalization of the trained network.
• Validates results by generating mock images and comparing them to real simulation outputs.

Experimental results

Research questions

• RQ1 Can neural ratio estimation accurately infer the minimum halo mass cutoff from N-body simulation images without explicit likelihood computation?
• RQ2 How well can a simple analytical halo model, informed by MNRE, reproduce the observed halo clustering and mass function in cosmological simulations?
• RQ3 Does the method remain robust under image transformations such as rotations, despite structural changes in input data?
• RQ4 To what extent can the trained model generate realistic mock images that resemble actual N-body simulation outputs?
• RQ5 What are the limitations of the current toy model in capturing non-Gaussian or filamentary structures in dark matter haloes?

Key findings

• The method successfully reconstructs the halo mass function cutoff (log10 cutoff) with high accuracy, where the true value lies within the 1σ and 2σ credible intervals in most cases.
• The model generates mock images that visually resemble the original N-body simulation images, indicating strong generative fidelity.
• Despite significant structural changes due to image rotation, the inferred posteriors remain highly stable, demonstrating robustness to data augmentation.
• The approach recovers the number of haloes with reasonable accuracy, though some deficiencies emerge in highly clustered regions, particularly for low-mass haloes.
• The results suggest that the current toy model, based on Gaussian random fields, is insufficient for capturing non-Gaussian features like filaments, indicating a need for more complex clustering models.
• The method is computationally feasible, with image generation taking ~1 second per 2000-halo image, enabling scalable simulation of thousands of mocks.