A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian
Processes
M. Ho, S. Bird, and C. Shelton. (2021)cite arxiv:2105.01081Comment: 17 pages, 17 figures, 1 table. Code available in https://github.com/jibanCat/matter_multi_fidelity_emu.
Abstract
We present methods for emulating the matter power spectrum which effectively
combine information from cosmological $N$-body simulations at different
resolutions. An emulator allows estimation of simulation output by
interpolating across the parameter space of a handful of simulations. We
present the first implementation of multi-fidelity emulation in cosmology,
where many low-resolution simulations are combined with a few high-resolution
simulations to achieve an increased emulation accuracy. The power spectrum's
dependence on cosmology is learned from the low-resolution simulations, which
are in turn calibrated using high-resolution simulations. We show that our
multi-fidelity emulator can achieve percent-level accuracy on average with only
$3$ high-fidelity simulations and outperforms a single-fidelity emulator that
uses $11$ simulations. With a fixed number of high-fidelity training
simulations, we show that our multi-fidelity emulator is $100$ times
better than a single-fidelity emulator at $k 2 \,hMpc^-1$,
and $20$ times better at $3 k < 6.4 \,hMpc^-1$.
Multi-fidelity emulation is fast to train, using only a simple modification to
standard Gaussian processes. Our proposed emulator shows a new way to predict
non-linear scales by fusing simulations from different fidelities.
Description
A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian Processes
%0 Generic
%1 ho2021multifidelity
%A Ho, Ming-Feng
%A Bird, Simeon
%A Shelton, Christian R.
%D 2021
%K library
%T A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian
Processes
%U http://arxiv.org/abs/2105.01081
%X We present methods for emulating the matter power spectrum which effectively
combine information from cosmological $N$-body simulations at different
resolutions. An emulator allows estimation of simulation output by
interpolating across the parameter space of a handful of simulations. We
present the first implementation of multi-fidelity emulation in cosmology,
where many low-resolution simulations are combined with a few high-resolution
simulations to achieve an increased emulation accuracy. The power spectrum's
dependence on cosmology is learned from the low-resolution simulations, which
are in turn calibrated using high-resolution simulations. We show that our
multi-fidelity emulator can achieve percent-level accuracy on average with only
$3$ high-fidelity simulations and outperforms a single-fidelity emulator that
uses $11$ simulations. With a fixed number of high-fidelity training
simulations, we show that our multi-fidelity emulator is $100$ times
better than a single-fidelity emulator at $k 2 \,hMpc^-1$,
and $20$ times better at $3 k < 6.4 \,hMpc^-1$.
Multi-fidelity emulation is fast to train, using only a simple modification to
standard Gaussian processes. Our proposed emulator shows a new way to predict
non-linear scales by fusing simulations from different fidelities.
@misc{ho2021multifidelity,
abstract = {We present methods for emulating the matter power spectrum which effectively
combine information from cosmological $N$-body simulations at different
resolutions. An emulator allows estimation of simulation output by
interpolating across the parameter space of a handful of simulations. We
present the first implementation of multi-fidelity emulation in cosmology,
where many low-resolution simulations are combined with a few high-resolution
simulations to achieve an increased emulation accuracy. The power spectrum's
dependence on cosmology is learned from the low-resolution simulations, which
are in turn calibrated using high-resolution simulations. We show that our
multi-fidelity emulator can achieve percent-level accuracy on average with only
$3$ high-fidelity simulations and outperforms a single-fidelity emulator that
uses $11$ simulations. With a fixed number of high-fidelity training
simulations, we show that our multi-fidelity emulator is $\simeq 100$ times
better than a single-fidelity emulator at $k \leq 2 \,h\textrm{Mpc}{^{-1}}$,
and $\simeq 20$ times better at $3 \leq k < 6.4 \,h\textrm{Mpc}{^{-1}}$.
Multi-fidelity emulation is fast to train, using only a simple modification to
standard Gaussian processes. Our proposed emulator shows a new way to predict
non-linear scales by fusing simulations from different fidelities.},
added-at = {2021-05-05T07:39:09.000+0200},
author = {Ho, Ming-Feng and Bird, Simeon and Shelton, Christian R.},
biburl = {https://www.bibsonomy.org/bibtex/28fe4dacdfc95d33d152487f1b0a990b3/gpkulkarni},
description = {A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian Processes},
interhash = {4a297f96668fc60fc2daf292f535ed69},
intrahash = {8fe4dacdfc95d33d152487f1b0a990b3},
keywords = {library},
note = {cite arxiv:2105.01081Comment: 17 pages, 17 figures, 1 table. Code available in https://github.com/jibanCat/matter_multi_fidelity_emu},
timestamp = {2021-05-05T07:39:09.000+0200},
title = {A Multi-Fidelity Emulator for the Matter Power Spectrum using Gaussian
Processes},
url = {http://arxiv.org/abs/2105.01081},
year = 2021
}