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

TL;DR

This paper introduces an interpretable, physics-informed machine learning emulator for the linear matter power spectrum that achieves high accuracy and physical consistency across standard and modified gravity cosmologies.

Contribution

It develops a symbolic regression-based framework combining domain knowledge and genetic algorithms to produce compact, accurate, and physically motivated analytic expressions for the matter power spectrum.

Findings

Achieves sub-percent errors across a broad scale range.

Successfully models BAO oscillations with physics-informed corrections.

Extends to modified gravity models with 1.5-1.8% accuracy.

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.