[Paper Review] Emulating cosmological multifields with generative adversarial networks

Sambatra Andrianomena, Francisco Villaescusa-Navarro+1 more|arXiv (Cornell University)|Nov 9, 2022

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper proposes a conditional generative adversarial network (GAN) to rapidly generate cosmological multifield images—gas density (Mgas), neutral hydrogen (HI), and magnetic field (B)—from hydrodynamic simulations in the CAMELS project. The GAN successfully reproduces key statistical properties, including pixel distribution, power spectra, and cross-correlations, across all three fields, enabling fast, accurate emulation of complex astrophysical simulations with high fidelity to the original data.

ABSTRACT

We explore the possibility of using deep learning to generate multifield images from state-of-the-art hydrodynamic simulations of the CAMELS project. We use a generative adversarial network to generate images with three different channels that represent gas density (Mgas), neutral hydrogen density (HI), and magnetic field amplitudes (B). The quality of each map in each example generated by the model looks very promising. The GAN considered in this study is able to generate maps whose mean and standard deviation of the probability density distribution of the pixels are consistent with those of the maps from the training data. The mean and standard deviation of the auto power spectra of the generated maps of each field agree well with those computed from the maps of IllustrisTNG. Moreover, the cross-correlations between fields in all instances produced by the emulator are in good agreement with those of the dataset. This implies that all three maps in each output of the generator encode the same underlying cosmology and astrophysics.

Motivation & Objective

• To accelerate the generation of cosmological multifield images from computationally expensive hydrodynamic simulations.
• To develop a deep generative model that preserves statistical properties—such as power spectra and cross-correlations—across multiple physical fields.
• To enable fast, scalable simulation of multiwavelength data for use in cosmological inference and survey pipeline design.
• To explore whether GANs can avoid mode collapse while generating complex, correlated astrophysical fields.
• To lay the foundation for a conditional generative model that can later be trained to predict outputs based on cosmological and astrophysical parameters.

Proposed method

• The model uses a conditional GAN with Skip-Layer Excitation (SLE) modules to enable gradient flow and high-resolution feature learning across multiple scales (4×4, 8×8, 16×16, 64×64, 128×128, 256×256).
• The generator employs channel-wise multiplications between low- and high-resolution feature maps via learnable weights, as defined in equation (1): $\mathbf{y} = \mathcal{F}(\mathbf{x}_{\text{low}}, \mathbf{W}) \cdot \mathbf{x}_{\text{high}}$.
• The discriminator is structured as an encoder with three decoders, trained via reconstruction loss on real images to enhance feature extraction, minimizing $\mathcal{L}_{\text{recons}} = \mathbb{E}_{\mathbf{f} \sim D(\mathbf{x})} [||\mathcal{G}(\mathbf{f}) - \mathcal{T}(\mathbf{x})||]$.
• The model is trained on 15,000 256×256 multifield images from the CAMELS Multifield Dataset, each with three channels representing Mgas, HI, and B at z=0.
• Latent space interpolation is used to verify smooth transitions between generated images, indicating absence of mode collapse.
• Statistical validation is performed using pixel-wise probability density functions (PDFs), auto- and cross-power spectra, and relative error metrics across 1,500 real and generated images.

Experimental results

Research questions

• RQ1 Can a GAN generate multifield cosmological images that preserve the statistical properties of individual fields, such as PDFs and power spectra?
• RQ2 To what extent does the GAN maintain cross-correlations between different physical fields (e.g., Mgas, HI, B) in the generated outputs?
• RQ3 Does the model avoid mode collapse during training, as evidenced by smooth latent space interpolation and consistent statistical outputs?
• RQ4 How well does the GAN reproduce the effects of cosmic variance and variations in cosmological and astrophysical parameters across the generated images?
• RQ5 Can the GAN serve as a fast, accurate emulator for hydrodynamic simulations in multiwavelength cosmology?

Key findings

• The GAN-generated maps exhibit mean and standard deviation of pixel probability density functions that are in strong agreement with the true simulation data across all three fields.
• The auto-power spectra of the generated maps match those of the real maps with relative error below 10% on large scales (k < 10 h/Mpc), with larger deviations only on small scales.
• The cross-power spectra between fields (e.g., Mgas–HI, HI–B) in the generated images are in excellent agreement with the real data, indicating preserved phase coherence and physical consistency.
• Latent space interpolation produces smooth transitions between generated images, confirming the absence of mode collapse and a continuous, meaningful latent representation.
• The model generates high-fidelity multifield images orders of magnitude faster than full hydrodynamic simulations, enabling rapid exploration of parameter space.
• Despite strong statistical agreement, minor discrepancies are observed in the tails of the PDF distributions, suggesting some limitations in capturing extreme-value statistics.