PERoKF: Physics-Enhanced Super-Resolution of Kolmogorov Flow

Fri, 19 Dec 2025 00:00:00 +0000

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

Physics-derived feature augmentation

Laplacian, streamfunction, velocity components, nonlinear advection terms

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.

Fluid Dynamics |