Model-Driven Conditional Fourier Neural Operator for Spectrum-Consistent Synthetic Turbulence Generation

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid dynamics and for broadband aeroacoustic noise prediction. Data-driven turbulence synthesis with neural networks has emerged as a promising direction. However, generating flow fields that match prescribed energy spectra across wide physical regimes remains challenging. Existing data-driven methods typically rely on expensive reliable datasets with limited generalization and are prone to regression-to-the-mean when trained in the spatial domain. To address these issues, the MD-CFNO is proposed with three components: a model-driven data construction strategy is adopted to improve interpretability and broaden the generalizable parameter regime; conditional stochastic generation is integrated into the Fourier neural operator architecture to alleviate regression-to-the-mean effects; and a composite loss is introduced to accelerate convergence and enhance spectral fidelity. Results show that the proposed MD-CFNO generates spectrum-consistent synthetic turbulence and achieves robust performance under both interpolation and out-of-distribution extrapolation conditions. This study provides a model-driven perspective on synthetic turbulence, showing the advantages of Fourier neural operators for conditional generation.