Cutting corners: Hypersphere sampling as a new standard for cosmological emulators

TL;DR

This paper introduces hypersphere sampling for cosmological emulators, focusing on high-likelihood regions to improve efficiency and accuracy over traditional Latin hypercube sampling, especially in high-dimensional parameter spaces.

Contribution

It presents a novel hypersphere sampling algorithm aligned with parameter correlations, enhancing emulator training efficiency and accuracy in cosmology.

Findings

Achieves similar or better precision with over ten times fewer data points.

Reduces computational costs significantly compared to Latin hypercube sampling.

Effective for complex, high-dimensional cosmological models.

Abstract

Cosmological emulators of observables such as the Cosmic Microwave Background (CMB) spectra and matter power spectra commonly use training data sampled from a Latin hypercube. This method often incurs high computational costs by covering less relevant parts of the parameter space, especially in high dimensions where only a small fraction of the parameter space yields a significant likelihood. In this paper, we introduce hypersphere sampling, which instead concentrates sample points in regions with higher likelihoods, significantly enhancing the efficiency and accuracy of emulators. A novel algorithm for sampling within a high-dimensional hyperellipsoid aligned with axes of correlation in the cosmological parameters is presented. This method focuses the distribution of training data points on areas of the parameter space that are most relevant to the models being tested, thereby avoiding the computational redundancies common in Latin hypercube approaches. Comparative analysis using the \textsc{connect} emulation tool demonstrates that hypersphere sampling can achieve similar or improved emulation precision with more than an order of magnitude fewer data points and thus less computational effort than traditional methods. This was tested for both the $\Lambda$CDM model and a 5-parameter extension including Early Dark Energy, massive neutrinos, and additional ultra-relativistic degrees of freedom. Our results suggest that hypersphere sampling holds potential as a more efficient approach for cosmological emulation, particularly suitable for complex, high-dimensional models.