Supplementary Material

Dark Quest II: A Wide-Coverage Neural Network Emulator of the Nonlinear Matter Power Spectrum Across Extended Cosmologies

Satoshi Tanaka, Takahiro Nishimichi, and Yosuke Kobayashi

This website provides supplementary material for the emulator-comparison analysis in the DarkEmulator2 paper. It contains parameter-range comparisons, fiducial-cosmology tests, cross-comparisons among public nonlinear matter power spectrum emulators, comparisons with fitting formulas, and auxiliary checks related to the Boltzmann-code inputs.

The materials are intended to document the calculations underlying the comparison section of the paper and to provide additional diagnostic plots that are not included in the main text.

• Paper: Dark Quest II: A Wide-Coverage Neural Network Emulator of the Nonlinear Matter Power Spectrum Across Extended Cosmologies
• arXiv: 2605.28596
• Journal DOI: forthcoming
• GitHub repository: dark_emulator2_public
• PyPI: dark-emulator2
• Example notebook: Comparison of public matter-power-spectrum emulators

Parameter-space coverage of public emulators

• These panels compare the parameter-space coverage of public nonlinear matter power-spectrum emulators.
• For each parameter, horizontal segments show the supported range of each emulator.
  • Where necessary, we convert between physical densities and density parameters using \(\omega_i \equiv \Omega_i h^2\) (equivalently \(\Omega_i = \omega_i / h^2\)).
• In the right-hand panels:
  • Solid lines denote the ranges of “native” input parameters used in the design of the emulator.
  • Dashed lines indicate the ranges of derived parameters inferred from over 1,000 Monte Carlo samples of the input parameter space.
  • The gray vertical dotted line marks the fiducial cosmology adopted for DarkEmulator2.
  • Parameters extending beyond the frame of this diagram have their values printed near the corresponding bar.

Comparison at the DQ2 fiducial parameters

• Fiducial-parameter comparison

Comparison of public emulators with DE2

• PkANN (\(\nu w_0 \mathrm{CDM}\))
  • \(P_\mathrm{tot}\)
• FrankenEmu (\(w_0 \mathrm{CDM}\))
  • \(P_\mathrm{tot}\)
• Mira-Titan Universe II (\(\nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{cb}\)
• Mira-Titan Universe IV (\(\nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{cb}\)
• EuclidEmulator2 (\(\nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{lin,tot}\)
• BaccoEmu (\(\nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{cb}\), \(P_\mathrm{lin,tot}\), \(P_\mathrm{lin,cb}\)
• CSST Emulator (\(\nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{cb}\), \(P_\mathrm{lin,tot}\), \(P_\mathrm{lin,cb}\)
• Aemulus \(\nu\) (\(\nu w_0 \mathrm{CDM}\))
  • \(P_\mathrm{tot}\)
• GokuNEmu (\(N_\mathrm{eff} \alpha_s \nu w_0 w_a \mathrm{CDM}\))
  • \(P_\mathrm{tot}\), \(P_\mathrm{lin,tot}\)
• Aletheia (\(w_0 w_a \Omega_k \mathrm{CDM}\))
  • \(P_\mathrm{tot}\)

Pairwise emulator comparisons

• Pairwise comparison of total matter \(P(k)\). Each entry compares the row emulator with the column emulator.

row / column	DE2	EE2	BaccoEmu	MTU IV	Aemulus \(\nu\)	GokuNEmu	Aletheia	CSST Emulator
EE2	DE2 vs EE2	-	-	-	-	-	-	-
BaccoEmu	DE2 vs BaccoEmu	EE2 vs BaccoEmu	-	-	-	-	-	-
MTU IV	DE2 vs MTU IV	EE2 vs MTU IV	BaccoEmu vs MTU IV	-	-	-	-	-
Aemulus \(\nu\)	DE2 vs Aemulus \(\nu\)	EE2 vs Aemulus \(\nu\)	BaccoEmu vs Aemulus \(\nu\)	MTU IV vs Aemulus \(\nu\)	-	-	-	-
GokuNEmu	DE2 vs GokuNEmu	EE2 vs GokuNEmu	BaccoEmu vs GokuNEmu	MTU IV vs GokuNEmu	Aemulus \(\nu\) vs GokuNEmu	-	-	-
Aletheia	DE2 vs Aletheia	EE2 vs Aletheia	BaccoEmu vs Aletheia	MTU IV vs Aletheia	Aemulus \(\nu\) vs Aletheia	GokuNEmu vs Aletheia	-	-
CSST Emulator	DE2 vs CSST Emulator	EE2 vs CSST Emulator	BaccoEmu vs CSST Emulator	MTU IV vs CSST Emulator	Aemulus \(\nu\) vs CSST Emulator	GokuNEmu vs CSST Emulator	Aletheia vs CSST Emulator	-

Comparison with fitting functions

• HMcode
• Halofit

Boltzmann-code comparison

• CLASS linear P(k)

Parameter dependence of \(P_\mathrm{lin,class}\)

• \(w_0, w_a, \Omega_{\mathrm{k}}\) dependence