Frequency-structured cross-fidelity errors in multiscale flow reconstruction

Abstract

Coarse-grid, filtered, and downsampled flow fields often retain the dominant large-scale organization of a high-fidelity (HF) solution while losing localized gradients, interfaces, shear layers, corner vortices, and curved-wall details. We, therefore, examine cross-fidelity errors from a fluid-mechanics perspective and formulate HF recovery as a frequency-decoupled, multi-fidelity, physics-constrained reconstruction task. Fourier-enhanced multi-fidelity neural networks (FE-MFNN) combine a shared low-frequency backbone, a Fourier-enhanced cross-fidelity residual branch, adaptive Fourier-basis screening, and progressive physics-constrained training based on low-fidelity (LF) data, boundary information, and residuals of the governing partial differential equation (PDE). Direct LF–HF spectral diagnostics show that the Burgers and Allen–Cahn residuals contain substantially larger high-band energy fractions than their corresponding HF fields under the same 75% cumulative-energy cutoff. Computational fluid dynamics diagnostics reveal weak co-location between cavity velocity-residual energy and HF vorticity but a stronger association between cylinder pressure-residual energy and HF pressure-gradient structures. Across scalar PDE benchmarks, lid-driven cavity flow, and subsonic compressible flow around a cylinder, FE-MFNN improves high-frequency reconstruction in shock-like, interface-dominated, and shear-layer-dominated cases and remains competitive for curved-boundary compressible flow. These results support frequency-decoupled reconstruction as a physically interpretable strategy in the tested multiscale-flow settings. The reported frequency structure is an empirical diagnostic of the archived coarse-resolution and separately exported LF datasets, not a universal physical law.