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

Hongyuan Lin, Shizhao Wang

TL;DR

The paper introduces MD-CFNO, a model-driven conditional Fourier neural operator for spectrum-consistent synthetic turbulence generation. By replacing DNS with a random Fourier model for data construction, conditioning the Fourier operator on physically meaningful parameters (TKE and dissipation), and enforcing spectrum-aligned losses in both spatial and wavenumber domains, the method achieves robust spectrum fidelity across interpolation and extrapolation regimes. Key findings show significant spectral accuracy and substantial computational speedups over traditional random Fourier models, alongside strong generalization to boundary conditions and stochastic variability within fixed conditions. The approach has strong potential for efficient inflow generation in CFD and broadband aeroacoustic predictions, with future work targeting anisotropic and spatiotemporal extensions.

Abstract

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.

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

TL;DR

The paper introduces MD-CFNO, a model-driven conditional Fourier neural operator for spectrum-consistent synthetic turbulence generation. By replacing DNS with a random Fourier model for data construction, conditioning the Fourier operator on physically meaningful parameters (TKE and dissipation), and enforcing spectrum-aligned losses in both spatial and wavenumber domains, the method achieves robust spectrum fidelity across interpolation and extrapolation regimes. Key findings show significant spectral accuracy and substantial computational speedups over traditional random Fourier models, alongside strong generalization to boundary conditions and stochastic variability within fixed conditions. The approach has strong potential for efficient inflow generation in CFD and broadband aeroacoustic predictions, with future work targeting anisotropic and spatiotemporal extensions.

Abstract

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.
Paper Structure (15 sections, 9 equations, 9 figures, 1 table)

This paper contains 15 sections, 9 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Overview
  4. Model-Driven Strategy
  5. Conditional Fourier Neural Operator
  6. Physics Constrained Loss Function
  7. Dataset Configuration and Implementation
  8. Dataset Configuration
  9. Implementation Details
  10. Results and Discussion
  11. Performance Validation
  12. Seed Generalization under Reference Condition
  13. Parametric Generalization to Boundary Conditions
  14. Impact of Loss Function
  15. Conclusions

Figures (9)

  • Figure 1: Schematic overview of the proposed MD-CFNO framework for spectrum-consistent synthetic turbulence generation.
  • Figure 2: Visualization of the model-driven data strategy and parameter space coverage.
  • Figure 3: Spectral accuracy comparison between the proposed MD-CFNO and C-UNet at the reference condition (Case 0).
  • Figure 4: Visual comparison of instantaneous velocity field contours at the reference condition (Case 0).
  • Figure 5: Quantitative comparison between the proposed MD-CFNO and RFM with varying mode numbers about computational efficiency and statistical accuracy.
  • ...and 4 more figures