# SIMR-NO

Rebuilding a 128×128 vorticity field from 8×8 observations is a 16× upscaling in which the coarse grid resolves only wavenumbers up to 4, so fine vortical structure must be inferred rather than interpolated. SIMR-NO splits the reconstruction into 32→64 and 64→128 stages, each adding a Fourier-layer residual correction gated by radial wavenumber on top of a bicubic base, with local convolutions recovering features beyond the truncated Fourier basis. Its mean relative error is 0.2506 on Kolmogorov-forced turbulence, below LapSRN, FNO and EDSR, and about 3% on decaying homogeneous isotropic turbulence at Re = 1000, 4000 and 8000, with little change across Reynolds number.

Rebuilding a 128×128 vorticity field from 8×8 observations is a 16× upscaling in which the coarse grid resolves only wavenumbers up to 4, so fine vortical structure must be inferred rather than interpolated. SIMR-NO splits the reconstruction into 32→64 and 64→128 stages, each adding a Fourier-layer residual correction gated by radial wavenumber on top of a bicubic base, with local convolutions recovering features beyond the truncated Fourier basis. Its mean relative error is 0.2506 on Kolmogorov-forced turbulence, below LapSRN, FNO and EDSR, and about 3% on decaying homogeneous isotropic turbulence at Re = 1000, 4000 and 8000, with little change across Reynolds number.