%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 }