Fidelity

Spectral density

Quantum mechanics

Algorithm

Gaussian

Emulation

Computational physics

Social psychology

Telecommunications

Economics

Power (physics)

Computer science

Acoustics

Statistical physics

Resolution (logic)

Spectrum (functional analysis)

Physics

Psychology

Gaussian process

Artificial intelligence

Gaussian random field

High fidelity

Economic growth

Monthly Notices of the Royal Astronomical Society

We present methods for emulating the matter power spectrum by combining information from cosmological $N$-body simulations at different resolutions. An emulator allows estimation of simulation output by interpolating across the parameter space of a limited number of simulations. We present the first implementation in cosmology of multi-fidelity emulation, 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 predicts high-fidelity counterparts to percent-level relative accuracy when using only $3$ high-fidelity simulations and outperforms a single-fidelity emulator that uses $11$ simulations, although we do not attempt to produce a converged emulator with high absolute accuracy. 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 $k \leq 2 h \mathrm{Mpc}^{-1}$, and $\simeq 20$ times better at $3 \leq k < 6.4 h \mathrm{Mpc}^{-1}$. 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.

Multifidelity emulation for the matter power spectrum using Gaussian processes