用物理约束的傅里叶-小波变换器,更准地重建复杂流场中的局部多尺度结构。
A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling

- 融合傅里叶-小波谱编码与基于方程残差的物理偏置自注意力机制。
- 在圆柱尾流和流固耦合基准上,均达到最低均方误差(如2.70×10⁻⁴)。
- 特别擅长恢复近体区、尾流核心区等局部精细结构,适合工程流场建模。
物理信息代理模型可加速计算流体力学仿真,但现有方法对全局流型建模较好,局部多尺度结构复现能力不足。本文提出一种物理信息引导的傅里叶-小波变换器,用于真实流场中下一步速度场重建。该方法结合混合傅里叶-小波谱编码与基于偏微分方程残差诊断的物理偏置自注意力,并通过掩码物理预测与方程一致性预测实现自监督预训练。在圆柱尾流与流固耦合两个真实基准测试中,所有方法采用统一局部评估协议,对比了谱方法、Transformer、算子学习及物理信息神经网络基线。圆柱尾流任务中,该模型取得最佳综合精度,全通道归一化均方误差为0.05875,皮尔逊相关系数达0.97019;流固耦合任务中,全通道归一化均方误差低至2.70×10⁻⁴,优于最强基线的4.02×10⁻⁴。组件级场比较与尺度分离诊断表明,其对近体区、尾流核心区及远尾流特征的恢复能力显著增强。结果证明该模型在保持实用精度-成本权衡的前提下,提升了真实流场重建性能。
原文摘要 · Abstract (English)
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.
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