A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling

2026-06-23

AI Summary

Existing physics-informed surrogate models struggle to accurately capture local multiscale flow structures. This work proposes a novel Transformer architecture that integrates a Fourier–wavelet hybrid spectral encoding with a physics-biased self-attention mechanism guided by partial differential equation (PDE) residual diagnostics. A self-supervised pretraining strategy is further introduced, combining masked physical prediction with equation consistency prediction. The proposed method substantially enhances the modeling of localized flow features and achieves state-of-the-art performance on canonical benchmarks for cylinder wake and fluid–structure interaction problems, yielding normalized mean squared errors of 0.05875 and 2.70×10⁻⁴, respectively, and a Pearson correlation coefficient of 0.97019. It faithfully reconstructs key flow structures, including near-body regions, the wake core, and far-wake zones.

Abstract

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of $2.70 \times 10^{-4}$, compared with $4.02 \times 10^{-4}$ for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

Problem

• computational fluid dynamics
• multiscale structures
• physics-informed surrogate modeling
• localized flow features
• velocity-field reconstruction

Innovation

• Physics-Informed Machine Learning
• Fourier-Wavelet Hybrid Encoding
• Multiscale CFD Surrogate Modeling
• PDE-Residual-Guided Attention
• Self-Supervised Pretraining