这个新模型用傅里叶加小波做流体模拟，比传统方法更准，尾流细节抓得更好，误差直接砍半。
该论文提出一种物理信息傅里叶-小波Transformer，用于计算流体动力学替代建模。方法结合了混合傅里叶-小波谱编码和基于PDE残差诊断的物理偏置自注意力机制，并通过遮罩物理预测和方程一致性预测进行自监督预训练。在圆柱尾流基准上，模型的全通道归一化均方误差为0.05875，皮尔逊相关系数为0.97019。在流固耦合基准上，全通道归一化均方误差为2.70×10⁻⁴，而最强基线为4.02×10⁻⁴。组件级场比较和尺度分离诊断显示，模型更好地恢复了近体、尾流核心和远尾流等局部尾流结构。
A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling
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.