Symbolic Emulators for Cosmology: Accelerating Cosmological Analyses Without Sacrificing Precision

TL;DR

This paper introduces expanded symbolic emulators for cosmological models that are faster and more memory-efficient, enabling precise and scalable parameter inference without sacrificing accuracy.

Contribution

The authors develop and validate new symbolic emulators covering relevant cosmological parameter ranges, with approximations that are highly accurate and significantly faster than traditional methods.

Findings

Symbolic emulators achieve better than 0.001% accuracy for hypergeometric functions.

Emulators produce consistent cosmological constraints in DES-like analyses.

Speed and memory improvements enable scalable likelihood-based inference.

Abstract

In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct numerical simulations. Symbolic emulators have emerged as promising alternatives to numerical approaches, delivering comparable accuracy with significantly faster evaluation times. While previous symbolic emulators were limited to relatively narrow prior ranges, we expand these to cover the parameter space relevant for current cosmological analyses. We introduce approximations to hypergeometric functions used for the $\Lambda$CDM comoving distance and linear growth factor which are accurate to better than 0.001% and 0.05%, respectively, for all redshifts and for $\Omega_{\rm m} \in [0.1, 0.5]$. We show that integrating symbolic emulators into a Dark Energy Survey-like $3\times2$pt analysis produces cosmological constraints consistent with those obtained using standard numerical methods. Our symbolic emulators offer substantial improvements in speed and memory usage, demonstrating their practical potential for scalable, likelihood-based inference.