Introduction

What is Goku-ELG?

Goku-ELG is a cosmological emulator for emission-line galaxies (ELGs), built using the GOKU simulation suite. It provides a fast and accurate surrogate model for predicting galaxy clustering statistics across a wide range of cosmological parameters.

The Science Behind It

For Astrophysicists

Resolving emission-line galaxies in N-body simulations requires high resolution, while achieving high-fidelity clustering statistics demands large volumes. We address both challenges efficiently by using machine learning models trained on the GOKU simulation suite (Yang et al. 2025).

Our method employs a multi-fidelity Gaussian Process model (Kennedy & O’Hagan 2000, Ho et al. 2021), along with elements of the Stochastic Variational GP framework, extended to support datasets with varying uncertainty levels through a modified likelihood.

Technical Approach

The emulator combines several advanced techniques:

  1. Bayesian Experimental Design: Strategic selection of simulation runs in the parameter space

  2. Multi-fidelity Gaussian Processes: Leveraging simulations at different resolutions and volumes

  3. Modified Stochastic Variational Framework: Handling datasets with heterogeneous uncertainties

  4. Halo Model Framework: Converting halo statistics to observable galaxy clustering

Key Summary Statistics

The emulator provides predictions for:

  • Halo Mass Function (HMF): \(\phi(M) dM\) - the abundance of dark matter halos as a function of mass

  • Halo-Halo Correlation Function: \(\xi_{hh}(r, M_{th1}, M_{th2})\) - spatial clustering of halos

  • Galaxy-Galaxy Correlation Function: \(\xi_{gg}(r)\) - observable galaxy clustering

  • Projected Correlation Function: \(w_p(r_p)\) - projected galaxy clustering

Computational Pipeline

The computational flow follows this sequence:

HMF Emulator → ϕ(M) dM
                ↓
Halo-Halo ξ Emulator → ξ_hh(M_th1, M_th2)
                        ↓
Hankel Transform → P_hh(k, M_th1, M_th2)
                   ↓
HOD Model → P_gg(k)
            ↓
Inverse Hankel Transform → ξ_gg(r)

Cosmological Parameters

The emulator covers a 10-dimensional parameter space:

  1. \(\Omega_m\) - Total matter density

  2. \(\Omega_b\) - Baryon density

  3. \(h\) - Hubble parameter

  4. \(A_s\) - Scalar amplitude

  5. \(n_s\) - Scalar spectral index

  6. \(w_0\) - Dark energy equation of state (present)

  7. \(w_a\) - Dark energy equation of state (evolution)

  8. \(N_{ur}\) - Effective number of ultra-relativistic species

  9. \(\alpha_s\) - Running of spectral index

  10. \(m_\nu\) - Neutrino mass

Performance Validation

Our emulator achieves:

  • < 1% accuracy in cross-validation tests for galaxy-galaxy clustering

  • Percent-level precision for halo mass function predictions

  • Robust extrapolation within the trained parameter space

  • Fast evaluation: Orders of magnitude faster than running N-body simulations

Applications

Goku-ELG is designed for:

  • Cosmological parameter inference from galaxy surveys

  • Mock catalog generation for survey planning

  • Fisher forecasts for upcoming surveys

  • Bayesian inference with MCMC or nested sampling

  • Rapid prototyping of galaxy clustering models

Target Surveys

This emulator is particularly suited for:

  • HETDEX (Hobby-Eberly Telescope Dark Energy Experiment)

  • DESI (Dark Energy Spectroscopic Instrument)

  • Euclid

  • Roman Space Telescope

  • Other emission-line galaxy surveys