Interpretable and physics-informed emulator for the linear matter power spectrum from machine learning

Abstract

We present an interpretable emulator for the linear matter power spectrum (MPS) in the standard cosmological model $\Lambda$CDM, constructed via a physics-informed symbolic regression framework. By combining domain knowledge with a machine learning technique known as genetic algorithms, we explore the space of analytic expressions to derive closed-form, smooth, physically motivated approximations of the MPS that match the accuracy of standard broadband reconstruction methodologies such as the Savitzky-Golay filter. Building upon this baseline, we incorporate transparent oscillatory corrections informed by the physics of baryon acoustic oscillations (BAO). The resulting expression delivers mean sub-percent fractional errors across a broad range of scales ($k\in [10^{-5},1.5]h{\mathrm{Mpc}}^{-1}$) with an average deviation of $\sim 0.4\%$ when tested against spectra computed with a Boltzmann solver. Moreover, a comparable level of fractional deviation is maintained on smaller scales when the GA-derived formulation is used as input to the nonlinear emulator halofit. To illustrate the versatility of the framework beyond $\Lambda$CDM, we apply it to a representative $f(R)$ gravity model. Rather than training a general modified-gravity emulator, we compute the corresponding linear spectra with a Boltzmann solver and fit a parametric deformation of the $\Lambda$CDM smoothed component. This procedure achieves average errors at the 1.5-1.8\% level and captures the leading modulation of the MPS induced by modified gravity, enabling a controlled study of its impact on the BAO scale. Our results provide compact, accurate, and physically motivated fitting functions for the linear MPS in both standard and MG cosmologies, offering a fast and transparent alternative to existing emulators for parameter inference and theoretical modeling in large-scale structure analyses.

Main: 25 pages. Several modifications with respect to v1. Accepted in PRD

References in corpus (68)

• Dynamics of dark energy
• Efficient Computation of CMB anisotropies in closed FRW models
• Modified Gravity and Cosmology
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Stable clustering, the halo model and nonlinear cosmological power spectra
• The 3D power spectrum of galaxies from the SDSS
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Massive neutrinos and cosmology
• Cosmology with cosmic shear observations: a review
• An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Dark Energy Survey Year 1 Results: Constraints on Extended Cosmological Models from Galaxy Clustering and Weak Lensing
• The Quijote simulations
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Observational systematics and baryon acoustic oscillations in the correlation function
• Searching for modified growth patterns with tomographic surveys
• The Coyote Universe Extended: Precision Emulation of the Matter Power Spectrum
• The BACCO Simulation Project: Exploiting the full power of large-scale structure for cosmology
• Euclid preparation: II. The EuclidEmulator -- A tool to compute the cosmology dependence of the nonlinear matter power spectrum
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System
• The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogues and Measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample
• Fractal Dimension as a measure of the scale of Homogeneity
• Constraints on deviations from $\Lambda$CDM within Horndeski gravity
• Fingerprinting dark energy
• A model independent null test on the cosmological constant
• What can Machine Learning tell us about the background expansion of the Universe?
• Euclid: Forecast constraints on the cosmic distance duality relation with complementary external probes
• On the road to percent accuracy IV: ReACT -- computing the non-linear power spectrum beyond $\Lambda$CDM
• MGCAMB with massive neutrinos and dynamical dark energy
• The effect of massive neutrinos on the matter power spectrum
• Genetic Algorithms and Supernovae Type Ia Analysis
• Cosmological constraints on multi-interacting dark matter
• hi_class: Background Evolution, Initial Conditions and Approximation Schemes
• Modeling the nonlinear clustering in modified gravity models I: A fitting formula for matter power spectrum of f(R) gravity
• Novel null tests for the spatial curvature and homogeneity of the Universe and their machine learning reconstructions
• Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results
• Hints of dark energy anisotropic stress using Machine Learning
• Unscreening Modified Gravity in the Matter Power Spectrum
• Measuring the 2D Baryon Acoustic Oscillation signal of galaxies in WiggleZ: Cosmological constraints
• Machine learning constraints on deviations from general relativity from the large scale structure of the Universe
• Machine Learning improved fits of the sound horizon at the baryon drag epoch
• Preparing for the Cosmic Shear Data Flood: Optimal Data Extraction and Simulation Requirements for Stage IV Dark Energy Experiments
• Fingerprinting Dark Energy III: distinctive marks of viscosity
• Kernel-Based Emulator for the 3D Matter Power Spectrum from CLASS
• Cosmological Constraints on sub-horizon scales modified gravity theories with MGCLASS II
• Machine learning forecasts of the cosmic distance duality relation with strongly lensed gravitational wave events
• New MGCAMB tests of gravity with CosmoMC and Cobaya
• Euclid: Forecast constraints on consistency tests of the $\Lambda$CDM model
• Cosmological parameter estimation with Genetic Algorithms
• Can dark energy viscosity be detected with the Euclid survey?
• A Genetic Algorithm for Astroparticle Physics Studies
• syren-halofit: A fast, interpretable, high-precision formula for the $\Lambda$CDM nonlinear matter power spectrum
• New Calabi-Yau Manifolds from Genetic Algorithms
• A precise symbolic emulator of the linear matter power spectrum
• Testing the $\Lambda$CDM paradigm with growth rate data and machine learning
• syren-new: Precise formulae for the linear and nonlinear matter power spectra with massive neutrinos and dynamical dark energy
• Using machine learning to compress the matter transfer function $T(k)$
• Improved analytical modeling of the non-linear power spectrum in modified gravity cosmologies
• Towards unveiling the large-scale nature of gravity with the wavelet scattering transform
• Machine learning unveils the linear matter power spectrum of modified gravity
• Solving the Schrodinger equation with genetic algorithms: a practical approach
• Tracking the validity of the quasi-static and sub-horizon approximations in modified gravity
• Optimal Gravitational-wave Follow-up Tiling Strategies Using a Genetic Algorithm