PERoKF: Physics-Enhanced Super-Resolution of Kolmogorov Flow

Team

• YiFan Cai
• YiRan Hu
• JiaCheng Zhu

Overview

PERoKF studies how to inject physics priors into modern neural networks for single-frame super-resolution of 2D Kolmogorov flow—without requiring temporal supervision. The goal is to recover fine-scale turbulent structures lost by downsampling.

• Input (LR): 128×128 vorticity
• Target (HR): 512×512 vorticity (4×)

Methods

We evaluate four model families (all operating on bicubic-upsampled LR inputs and predicting HR vorticity):

• CNN: lightweight hierarchical convolutional baseline
• UNet: multi-scale ResNet-style UNet (optional attention)
• FNO: Fourier Neural Operator with truncated spectral modes
• Diffusion: conditional DDPM with UNet backbone (x₀-prediction)

Physics-guided strategies

1. Physics-derived feature augmentation

• Laplacian, streamfunction, velocity components, nonlinear advection terms

2. Physics-consistency loss

• Navier–Stokes residual loss using the same pseudo-spectral operator as data generation
• Enforces consistency via implied time derivatives

Key findings (high-level)

• Physics-consistency loss consistently improves physical accuracy (e.g., lower PDE residual and energy spectrum error) and can accelerate diffusion convergence.
• Physics features alone are not consistently beneficial and may destabilize training.
• Combining both can improve accuracy but may introduce instability under limited compute.

Dataset & evaluation

Dataset: 2D Kolmogorov flow (HR 512×512 / LR 128×128), Reynolds numbers 1000/2000/3000, forcing wavenumbers 8/12/16.

Metrics:

• MSE (pixel reconstruction)
• Physics Consistency Error (PCE)
• Energy Spectrum Error (ESE)

Reproducibility

• Training configs and scripts are included in the repository.
• Visualization scripts compare HR/LR/reconstruction and energy spectra.