AI 中文总结
研究针对多尺度流体动力学，提出物理信息小波 - 傅里叶表示法，分离流场互补分量并融合输出，通过物理信息损失施加条件，经五个典型问题评估，该方法比其他方法能提高流动特征分辨率，为分析多尺度流动提供途径。
AI 中文摘要
多尺度流体流动包含局部流动结构，准确预测需兼顾全局守恒趋势和小尺度梯度。本研究通过物理信息小波 - 傅里叶（PIWF）表示来审视这些流动物理要求。该方法在物理信息神经表示中分离出流场的两个互补分量，经通道注意力融合输出，通过物理信息损失直接施加控制方程、初始条件和边界条件。在五个典型流体动力学问题上评估模型，结果表明PIWF相对于标准物理信息神经网络等能提高多种流动特征的分辨率，为分析多尺度流动现象提供了有用途径。
英文摘要
Multiscale fluid flows often contain localized flow structures, such as viscous shock layers, wet-dry fronts, steady viscous wakes, decaying vortical structures, and vortex-shedding patterns, whose accurate prediction requires the simultaneous preservation of global conservation trends and small-scale gradients. This study examines these flow-physics requirements through a physics-informed wavelet-Fourier (PIWF) representation for multiscale fluid dynamics. Instead of relying on a single monolithic neural approximator, the formulation separates two complementary components of the flow field within a physics-informed neural representation: long-range coherent modes through a Fourier-basis branch and localized steep-gradient or vortical features through a compactly supported wavelet branch. The outputs are fused with a residual multilayer perceptron using channel attention, and the governing equations, initial conditions, and boundary conditions are imposed directly through the physics-informed loss. The model is assessed on five canonical fluid-dynamics problems: Burgers' equation, the shallow water equations, Kovasznay flow, Taylor--Green vortex flow, and two-dimensional cylinder wake flow. The results show that PIWF improves the resolution of shock-like gradients, wet--dry interfaces, steady wake fields, decaying vortical structures, vorticity extrema, and broadband wake spectra relative to standard physics-informed neural networks and physics-informed Kolmogorov--Arnold networks. These findings indicate that a wavelet-Fourier physics-informed representation can provide a useful route for analyzing multiscale flow phenomena when high-fidelity interior reference data are limited or unavailable.
