Differentiable Fuzzy Cosmic-Web for Field Level Inference

Abstract

A comprehensive analysis of the cosmological large-scale structure derived from galaxy surveys involves field-level inference, which requires a forward modelling framework that simultaneously accounts for structure formation and tracer bias. While structure formation models are well-understood, the development of an effective field-level bias model remains challenging within Bayesian reconstruction methods, which we address in this work. To bridge this gap, we have developed a differentiable model that integrates augmented Lagrangian perturbation theory, nonlinear, nonlocal, and stochastic biasing. At the core of our approach is the HICOBIAN model, which provides a description of a field with a positive number of tracers while incorporating a long- and short-range nonlocal framework and deviations from Poissonity in the likelihood. A key insight of our model is that transitions between cosmic-web regions are inherently smooth, which we implement using sigmoid-based gradient operations. This enables a fuzzy, and, hence, differentiable hierarchical cosmic-web description, making the model well-suited for machine learning frameworks. We test the practical implementation of this model through GPU-accelerated computations implemented in JaX, the BRIDGE code, enabling scalable evaluation of complex biasing. Our approach accurately reproduces the primordial density field within associated error bars derived from Bayesian posterior sampling within a self-specified setting as validated by two- and three-point statistics in Fourier space. Furthermore, we demonstrate that the methodology approaches the maximum encoded information consistent with Poisson noise. We also demonstrate that the bias parameters of a higher-order nonlocal bias model can be accurately reconstructed within the Bayesian framework for bias models with eight parameters.

16 pages, 15 figures, accepted for publication at Astronomy and Astrophysics

References in corpus (70)

• Large-Scale Galaxy Bias
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
• Properties of Dark Matter Haloes in Clusters, Filaments, Sheets and Voids
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Solving Large Scale Structure in Ten Easy Steps with COLA
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
• Bayesian physical reconstruction of initial conditions from large scale structure surveys
• Gravity and Large-Scale Non-local Bias
• A Dynamical Classification of the Cosmic Web
• The Uchuu Simulations: Data Release 1 and Dark Matter Halo Concentrations
• FastPM: a new scheme for fast simulations of dark matter and halos
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Modeling the clustering and halo occupation distribution of BOSS-CMASS galaxies in the Final Data Release
• Halo Stochasticity from Exclusion and non-linear Clustering
• Modelling Baryon Acoustic Oscillations with Perturbation Theory and Stochastic Halo Biasing
• ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics
• Physical Bayesian modelling of the non-linear matter distribution: new insights into the Nearby Universe
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Modeling Biased Tracers at the Field Level
• The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space Telescope
• Fast Hamiltonian sampling for large scale structure inference
• Past and present cosmic structure in the SDSS DR7 main sample
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• The Initial Conditions of the Universe from Constrained Simulations
• Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
• The Abacus Cosmos: A Suite of Cosmological N-body Simulations
• Reconstructing the Cosmic Velocity and Tidal Fields with Galaxy Groups Selected from the Sloan Digital Sky Survey
• Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7
• Reconstructing the Initial Density Field of the Local Universe: Method and Test with Mock Catalogs
• UNIT project: Universe $N$-body simulations for the Investigation of Theoretical models from galaxy surveys
• Unmasking the Masked Universe: the 2M++ catalogue through Bayesian eyes
• Comparing approximate methods for mock catalogues and covariance matrices II: Power spectrum multipoles
• Dark matter statistics for large galaxy catalogs: power spectra and covariance matrices
• Recovering the nonlinear density field from the galaxy distribution with a Poisson-Lognormal filter
• Constraining the halo bispectrum in real and redshift space from perturbation theory and non-linear stochastic bias
• A halo bias function measured deeply into voids without stochasticity
• Linear redshift space distortions for cosmic voids based on galaxies in redshift space
• Super-resolution emulator of cosmological simulations using deep physical models
• Simulating Structure Formation of the Local Universe
• Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers
• Numerical integrators for the Hybrid Monte Carlo method
• Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Lyman alpha forest
• Multiscale Inference of Matter Fields and Baryon Acoustic Oscillations from the Ly-alpha Forest
• Cosmic Structure and Dynamics of the Local Universe
• FlowPM: Distributed TensorFlow Implementation of the FastPM Cosmological N-body Solver
• COSMIC BIRTH: Efficient Bayesian Inference of the Evolving Cosmic Web from Galaxy Surveys
• The cosmic web of the Local Universe: cosmic variance, matter content and its relation to galaxy morphology
• Estimating cosmic velocity fields from density fields and tidal tensors
• TARDIS Paper I: A Constrained Reconstruction Approach to Modeling the z~2.5 Cosmic Web Probed by Lyman-alpha Forest Tomography
• Extremely Metal-Poor Galaxies: The Environment
• BAM: Bias Assignment Method to generate mock catalogs
• Inferring high redshift large-scale structure dynamics from the Lyman-alpha forest
• BIRTH of the COSMOS Field: Primordial and Evolved Density Reconstructions During Cosmic High Noon
• Cosmology inference at the field level from biased tracers in redshift-space
• Optimal Reconstruction of Baryon Acoustic Oscillations for DESI 2024
• Constraining Primordial Non-Gaussianity with Post-reconstructed Galaxy Bispectrum in Redshift Space
• Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data
• Truthing the stretch: Non-perturbative cosmological realizations with multiscale spherical collapse
• Bayesian Inference of Initial Conditions from Non-Linear Cosmic Structures using Field-Level Emulators
• TARDIS Paper II: Synergistic Density Reconstruction from Lyman-alpha Forest and Spectroscopic Galaxy Surveys with Applications to Protoclusters and the Cosmic Web
• The bias of dark matter tracers: assessing the accuracy of mapping techniques
• Bayesian cosmic density field inference from redshift space dark matter maps
• Differentiable Cosmological Simulation with Adjoint Method
• Renormalisation of linear halo bias in N-body simulations
• The cosmic web connection to the dark matter halo distribution through gravity
• Mapping Lyman-alpha forest three-dimensional large scale structure in real and redshift space
• Bayesian redshift-space distortions correction from galaxy redshift surveys
• HyPhy: Deep Generative Conditional Posterior Mapping of Hydrodynamical Physics
• Fast simulation mapping: from standard to modified gravity cosmologies using the bias assignment method
• A universal and physically motivated threshold for Hessian-based cosmic web identification: V-Web case