SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolution

TL;DR

The paper introduces SIMR-NO, a novel spectral multi-resolution neural operator that significantly improves super-resolution of turbulent flow fields from coarse data, ensuring physically consistent reconstructions.

Contribution

It presents a hierarchical operator learning framework with spectral gating and local refinement, enhancing turbulence super-resolution beyond existing methods.

Findings

Achieves 26.04% mean relative error in turbulence super-resolution.

Reduces error by 31.7% over FNO and 26.0% over EDSR.

Faithfully reproduces energy and enstrophy spectra across wavenumbers.

Abstract

Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machine learning. Classical interpolation methods fail to recover missing fine-scale structures, while existing deep learning approaches rely on convolutional architectures that lack the spectral and multiscale inductive biases necessary for physically faithful reconstruction at large upscaling factors. We introduce the Spectrally-Informed Multi-Resolution Neural Operator (SIMR-NO), a hierarchical operator learning framework that factorizes the ill-posed inverse mapping across intermediate spatial resolutions, combines deterministic interpolation priors with spectrally gated Fourier residual corrections at each stage, and incorporates local refinement modules to recover fine-scale spatial features beyond the truncated Fourier basis. The proposed method is evaluated on Kolmogorov-forced two-dimensional turbulence, where $128\times128$ vorticity fields are reconstructed from extremely coarse $8\times8$ observations representing a $16\times$ downsampling factor. Across 201 independent test realizations, SIMR-NO achieves a mean relative $\ell_2$ error of $26.04\%$ with the lowest error variance among all methods, reducing reconstruction error by $31.7\%$ over FNO, $26.0\%$ over EDSR, and $9.3\%$ over LapSRN. Beyond pointwise accuracy, SIMR-NO is the only method that faithfully reproduces the ground-truth energy and enstrophy spectra across the full resolved wavenumber range, demonstrating physically consistent super-resolution of turbulent flow fields.