Translation and Rotation Equivariant Normalizing Flow (TRENF) for Optimal Cosmological Analysis

Abstract

Our universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work we develop Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise nonlinear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On nonlinear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

11 pages, 10 figures. Submitted to MNRAS. Comments welcome

References in corpus (4)

• ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics
• Nuisance hardened data compression for fast likelihood-free inference
• Lossless, Scalable Implicit Likelihood Inference for Cosmological Fields
• Fanaroff-Riley classification of radio galaxies using group-equivariant convolutional neural networks

Cited by in corpus (27)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• The DAWES review 10: The impact of deep learning for the analysis of galaxy surveys
• Field Level Neural Network Emulator for Cosmological N-body Simulations
• Exploring the likelihood of the 21-cm power spectrum with simulation-based inference
• Cosmology inference at the field level from biased tracers in redshift-space
• EFTofLSS meets simulation-based inference: ${\sigma }_8$ from biased tracers
• How informative are summaries of the cosmic 21-cm signal?
• A comparative study of cosmological constraints from weak lensing using Convolutional Neural Networks
• Fast and realistic large-scale structure from machine-learning-augmented random field simulations
• Cosmological constraints from weak lensing scattering transform using HSC Y1 data
• PopSED: Population-Level Inference for Galaxy Properties from Broadband Photometry with Neural Density Estimation
• Machine Learning and Cosmology
• Reconstructing the Universe with Variational self-Boosted Sampling
• A field-level emulator for modeling baryonic effects across hydrodynamic simulations
• Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures
• Inferring subhalo effective density slopes from strong lensing observations with neural likelihood-ratio estimation
• Massive $\nu$s through the CNN lens: interpreting the field-level neutrino mass information in weak lensing
• Field-level Reconstruction from Foreground-Contaminated 21-cm Maps
• Neural style transfer of weak lensing mass maps
• Interpreting Cosmological Information from Neural Networks in the Hydrodynamic Universe
• Detecting Modeling Bias with Continuous Time Flow Models on Weak Lensing Maps
• Generative modeling of convergence maps based on predicted one-point statistics
• Fast Baryonic Field Painting for Sunyaev-Zel'dovich Analyses: Transfer Function vs. Hybrid Effective Field Theory
• Replicating weak-lensing summary-statistic covariances with normalizing flows
• On the Connection between Field-Level Inference and $n$-point Correlation Functions
• D${}_4$CNN$\times$AnaCal: Physics-Informed Machine Learning for Accurate and Precise Weak Lensing Shear Estimation
• Fast Sampling of Cosmological Initial Conditions with Gaussian Neural Posterior Estimation