Learning the Universe: Learning to Optimize Cosmic Initial Conditions with Non-Differentiable Structure Formation Models

Abstract

Making the most of next-generation galaxy clustering surveys requires overcoming challenges in complex, non-linear modelling to access the significant amount of information at smaller cosmological scales. Field-level inference has provided a unique opportunity beyond summary statistics to use all of the information of the galaxy distribution. However, addressing current challenges often necessitates numerical modelling that incorporates non-differentiable components, hindering the use of efficient gradient-based inference methods. In this paper, we introduce Learning the Universe by Learning to Optimize (LULO), a gradient-free framework for reconstructing the 3D cosmic initial conditions. Our approach advances deep learning to train an optimization algorithm capable of fitting state-of-the-art non-differentiable simulators to data at the field level. Importantly, the neural optimizer solely acts as a search engine in an iterative scheme, always maintaining full physics simulations in the loop, ensuring scalability and reliability. We demonstrate the method by accurately reconstructing initial conditions from $M_{200\mathrm{c}}$ halos identified in a dark matter-only $N$-body simulation with a spherical overdensity algorithm. The derived dark matter and halo overdensity fields exhibit $\ge 80\%$ cross-correlation with the ground truth into the non-linear regime $k\sim 1h$ Mpc${}^{-1}$. Additional cosmological tests reveal accurate recovery of the power spectra, bispectra, halo mass function, and velocities. With this work, we demonstrate a promising path forward to non-linear field-level inference surpassing the requirement of a differentiable physics model.

20 pages, 15 figures. Updated to match version accepted by MNRAS (published 2025/08/06)

References in corpus (92)

• An overview of gradient descent optimization algorithms
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• MultiResUNet : Rethinking the U-Net Architecture for Multimodal Biomedical Image Segmentation
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• Toward a halo mass function for precision cosmology: the limits of universality
• The Rockstar Phase-Space Temporal Halo Finder and the Velocity Offsets of Cluster Cores
• Cosmology and Fundamental Physics with the Euclid Satellite
• Ahf: Amiga's Halo Finder
• Multi-scale initial conditions for cosmological simulations
• Large-Scale Galaxy Bias
• Euclid. I. Overview of the Euclid mission
• The evolution substructure I: a new identification method
• Simulating cosmic structure formation with the GADGET-4 code
• The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of Baryon Acoustic Oscillations between redshift 0.8 and 2.2
• Solving Large Scale Structure in Ten Easy Steps with COLA
• The Quijote simulations
• Bayesian physical reconstruction of initial conditions from large scale structure surveys
• The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations
• The FLAMINGO project: cosmological hydrodynamical simulations for large-scale structure and galaxy cluster surveys
• Learning to Predict the Cosmological Structure Formation
• FastPM: a new scheme for fast simulations of dark matter and halos
• Large-scale dark matter simulations
• Minimizing the stochasticity of halos in large-scale structure surveys
• The MillenniumTNG Project: The hydrodynamical full physics simulation and a first look at its galaxy clusters
• 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
• ELUCID - Exploring the Local Universe with reConstructed Initial Density field III: Constrained Simulation in the SDSS Volume
• How to suppress the shot noise in galaxy surveys
• The Hestia project: simulations of the Local Group
• Past and present cosmic structure in the SDSS DR7 main sample
• Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints
• The Initial Conditions of the Universe from Constrained Simulations
• The Pantheon+ Analysis: Evaluating Peculiar Velocity Corrections in Cosmological Analyses with Nearby Type Ia Supernovae
• Towards optimal extraction of cosmological information from nonlinear data
• Are peculiar velocity surveys competitive as a cosmological probe?
• Velocity correction for Hubble constant measurements from standard sirens
• The DAWES review 10: The impact of deep learning for the analysis of galaxy surveys
• Recurrent Inference Machines for Solving Inverse Problems
• Reconstructing the Initial Density Field of the Local Universe: Method and Test with Mock Catalogs
• Unmasking the Masked Universe: the 2M++ catalogue through Bayesian eyes
• Cosmological Reconstruction From Galaxy Light: Neural Network Based Light-Matter Connection
• A rigorous EFT-based forward model for large-scale structure
• Cosmological Forecasts for Combined and Next Generation Peculiar Velocity Surveys
• Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers
• Bayesian analysis of the dynamic cosmic web in the SDSS galaxy survey
• Cosmological inference from Bayesian forward modelling of deep galaxy redshift surveys
• How much information can be extracted from galaxy clustering at the field level?
• How Biased Are Halo Properties in Cosmological Simulations?
• FlowPM: Distributed TensorFlow Implementation of the FastPM Cosmological N-body Solver
• COSMIC BIRTH: Efficient Bayesian Inference of the Evolving Cosmic Web from Galaxy Surveys
• Field Level Neural Network Emulator for Cosmological N-body Simulations
• SIBELIUS-DARK: a galaxy catalogue of the Local Volume from a constrained realisation simulation
• TARDIS Paper I: A Constrained Reconstruction Approach to Modeling the z~2.5 Cosmic Web Probed by Lyman-alpha Forest Tomography
• Bayesian forward modelling of cosmic shear data
• Painting halos from cosmic density fields of dark matter with physically motivated neural networks
• Peculiar velocities in the local Universe: comparison of different models and the implications for $H_0$ and dark matter
• Second Data Release of the COSMOS Lyman-alpha Mapping and Tomographic Observation: The First 3D Maps of the Detailed Cosmic Web at 2.05<z<2.55
• Consistency tests of field level inference with the EFT likelihood
• Precision constrained simulation of the Local Universe
• A gradient based method for modeling baryons and matter in halos of fast simulations
• Predicting dark matter halo formation in N-body simulations with deep regression networks
• Predicted future fate of COSMOS galaxy protoclusters over 11 Gyr with constrained simulations
• BIRTH of the COSMOS Field: Primordial and Evolved Density Reconstructions During Cosmic High Noon
• Reconstructing Cosmological Initial Conditions from Late-Time Structure with Convolutional Neural Networks
• NECOLA: Towards a Universal Field-level Cosmological Emulator
• Exploring the posterior surface of the large scale structure reconstruction
• Galaxy clusters in simulations of the local Universe: a matter of constraints
• Neural physical engines for inferring the halo mass distribution function
• The primordial magnetic field in our cosmic backyard
• Effective cosmic density field reconstruction with convolutional neural network
• Bayesian Inference of Initial Conditions from Non-Linear Cosmic Structures using Field-Level Emulators
• Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling
• A hierarchical field-level inference approach to reconstruction from sparse Lyman-$\alpha$ forest data
• Field-level inference of galaxy intrinsic alignment from the SDSS-III BOSS survey
• Constraints on galileons from the positions of supermassive black holes
• Bayesian cosmic density field inference from redshift space dark matter maps
• Differentiable Cosmological Simulation with Adjoint Method
• Towards Accurate Field-Level Inference of Massive Cosmic Structures
• Improving constraints on primordial non-Gaussianity using neural network based reconstruction
• Reconstructing the Universe with Variational self-Boosted Sampling
• Field-Based Physical Inference From Peculiar Velocity Tracers
• Biased tracer reconstruction with halo mass information
• Constrained cosmological simulations of the Local Group using Bayesian hierarchical field-level inference
• $\text{PineTree}$: A generative, fast, and differentiable halo model for wide-field galaxy surveys
• Constrained Local UniversE Simulations (CLUES)
• The effect of local universe constraints on halo abundance and clustering
• Evaluating the variance of individual halo properties in constrained cosmological simulations
• Weak Lensing analysis of Abell 2390 using short exposures
• COmoving Computer Acceleration (COCA): $N$-body simulations in an emulated frame of reference
• Introducing cosmosTNG: simulating galaxy formation with constrained realizations of the COSMOS field
• Neural Network Reconstruction of Non-Gaussian Initial Conditions from Dark Matter Halos

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