无需求导即可从噪声数据中识别流体动力学机制。
Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure
- 用积分形式替代微分，避免数值求导带来的噪声放大。
- 在严重噪声下仍能准确识别动态一致的流体结构。
- 首次实现湍流管道流的第三阶方程数据驱动分解。
从复杂时空数据中提取可解释、局部化的物理机制是物理、生物和工程领域的基础挑战，但以往方法仅适用于干净模拟数据。核心障碍在于通过数值微分获取高质量梯度，该过程会放大噪声、对高阶方程发散，并在非规则几何上失效，限制了现有方法仅能处理低阶系统的清洁仿真。本文提出弱主导平衡（weak dominant balance），一种无导数框架，将控制方程投影至弱（积分）形式，将微分操作转移到光滑的解析测试函数上，保持原始数据不变。该方法在严重噪声下仍能准确识别系统模式，首次实现对湍流管道流的三阶偏微分方程的数据驱动分解，并在直接数值模拟与粒子图像测速（PIV）测量的波状通道流中得到一致分解结果，揭示了此前未被描述的动力学状态。弱主导平衡使机制级分析从仿真走向实测数据，为复杂物理系统提供了基于方程的直接解读路径。
原文摘要 · Abstract (English)
Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.
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