TY - JOUR
T1 - Cutting corners
T2 - hypersphere sampling as a new standard for cosmological emulators
AU - Nygaard, Andreas
AU - Holm, Emil Brinch
AU - Hannestad, Steen
AU - Tram, Thomas
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/10
Y1 - 2024/10
N2 - 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 make use of 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 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 ΛCDM 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.
AB - 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 make use of 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 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 ΛCDM 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.
KW - cosmological parameters from CMBR
KW - cosmological parameters from LSS
KW - cosmology of theories beyond the SM
KW - Machine learning
UR - http://www.scopus.com/inward/record.url?scp=85207721853&partnerID=8YFLogxK
U2 - 10.1088/1475-7516/2024/10/073
DO - 10.1088/1475-7516/2024/10/073
M3 - Journal article
AN - SCOPUS:85207721853
SN - 1475-7516
VL - 2024
JO - Journal of Cosmology and Astroparticle Physics
JF - Journal of Cosmology and Astroparticle Physics
IS - 10
M1 - 073
ER -