Super-Resolution in Cosmological Simulations
Date:
Overview
This talk, presented at the Reunión de Estudiantes de Astronomía (REA) 2025, introduces a super-resolution framework for cosmological simulations that combines deep generative models with the Wavelet Scattering Transform (WST) to enhance the resolution of dark-matter density fields.
The work addresses a key challenge in modern computational cosmology:
High-resolution N-body simulations are extremely expensive, while low-resolution runs lose crucial small-scale information.
By integrating WST into a residual generative architecture, the method recovers small-scale structure while preserving the statistical and physical properties of the underlying cosmological field.
Motivation
Cosmological simulations face an inherent trade-off:
- High resolution → extremely expensive CPU/GPU time + large storage
- Low resolution → loss of small-scale halos, filaments, and non-Gaussian structure
Existing deep-learning super-resolution approaches (GANs, VAEs, diffusion models) suffer from:
- Instability during training
- Hallucination of non-physical structures
- Loss of cosmological statistics
- Poor interpretability
(Slides 1–3)
Approach: Wavelet-Based Generative Super-Resolution
The method incorporates the Wavelet Scattering Transform (WST) into a deep residual architecture to stabilize training and preserve physical information.
Why WST?
- Captures multi-scale structure
- Stable to deformations and small translations
- Sensitive to non-Gaussian statistics
- Avoids phase reconstruction issues typical of Fourier-based approaches
(Slides 16–21)
WST coefficients serve as a statistical loss function that forces the network to match the high-resolution distribution of cosmological fields.
Dataset: Illustris Simulations
Training is performed using slices from the Illustris family of simulations:
- Illustris-3 → low-resolution input
- Illustris-2 → high-resolution target
Each slice:
- Thickness: 0.25 Mpc
- Paired dataset: 7200 LR/HR image pairs
(Slides 23–26)
Split into:
- 90% training
- 10% validation
- 800 images for testing
Network Architecture
The proposed architecture includes:
- Two feature extraction branches (LR features + WST features)
- Feature fusion layer
- n residual Squeeze-and-Excitation (SE) blocks
- Output reconstruction layer
(Slides 27–28)
Loss functions explored:
- L2 (MSE)
- Perceptual loss
- WST-based loss (best performance)
(Slides 29–32)
Training:
- Performed on an RTX 4090 (24 GB VRAM)
- ~8 hours per training run
(Slide 32)
Results
Qualitative Reconstruction
The model reconstructs higher-resolution structures that closely resemble Illustris-2, while avoiding hallucinations typical of GAN-based methods.
(Slides 33–36)
Power Spectrum Evaluation
A physically meaningful test is performed by comparing the recovered power spectrum P(k):
- Bicubic interpolation → severe loss of small-scale power
- L1/Perceptual loss → improved but imperfect
- WST loss → closest match to ground truth across a wide k-range, even up to k ≈ 5–6 h/Mpc
(Slide 36)
Peak and Valley Counts
The model also preserves higher-order morphological statistics like:
- Density of local maxima
- Density of local minima
(Slides 37–39)
Conclusions
- WST-based super-resolution produces physically consistent reconstructions of cosmological fields.
- Recovers statistical properties (P(k), peaks/valleys) better than standard approaches.
- Provides a more interpretable alternative to GANs and VAEs.
- Has potential to augment low-resolution simulations and reduce computational demands for large parameter scans.
(Slides 40–41)
Future Work
- Increase network capacity with more residual blocks
- Incorporate additional WST scales
- Extend to fully 3D super-resolution
- Train on larger, multi-institutional cosmology datasets
(Slide 41)