Prediction and understanding of the wall-shear stress modulation by non-linear interactions based on novel machine learning techniques

壁面湍流流动在工程和生物医学领域有着重要的应用。然而，它们的典型特征是高维，非线性和不稳定的动力学，在空间和时间上表现出丰富的多尺度现象。由于这些具有挑战性的特性，我们仍然缺乏对这些复杂流体的全面了解。对于大多数应用来说，一个关键因素是空间和时间分辨的壁面剪应力。除了提供摩擦阻力的测量-这是运输部门最重要的量-它还提供了对施加在刚性/柔性墙壁上的动态载荷的洞察，这在人类医学中至关重要。尽管它的意义，它仍然是非常困难的测量瞬时和空间分辨壁面剪应力分布。现有的大多数测量传感器是单向和/或一维设备，只能检测一个壁面剪应力分量在一个固定的位置。此外，空间分辨率和联合部署的传感器的最大数量通常是有限的，这是由于实验的约束所产生的辅助电子设备。因此，绝大多数针对调制壁面剪应力动力学的多尺度现象的调查的最新研究仅限于没有空间分辨率的时间相关数据，因此，不能提供复杂物理的全面图片。因此，该提案的总体目标是开发基于现代深度学习的算法，用于基于易于访问的速度测量来预测壁面剪应力。所设想的神经网络是专门设计来捕捉-不限制假设-复杂的非线性和不稳定的相互作用，负责壁面剪应力动态，并使它们解释为人类。特别是，该提案的目标是开发一种基于深度学习的架构，该架构专门设计用于学习从位于湍流壁边界流外层的二维速度场到瞬时空间分辨壁面剪应力分布的映射函数。互补的，一个可解释的数学表达式，它对应于固有的学习传递函数，通过符号回归从派生的潜在表示中提取。进一步研究了该表达式，以更深入地了解导致壁面剪应力调制的非线性相互作用。训练直接数值模拟数据，概括的设想的学习者证明了在外层和壁面剪切应力测量使用微柱剪切应力传感器的同时粒子图像测速测量的基础上。

Turbulent wall-bounded fluid flows are of significant importance for numerous engineering and biomedical applications. However, they are typically characterized by high-dimensional, non-linear, and unsteady dynamics that exhibit rich multi-scale phenomena in space and time. Due to such challenging characteristics, we still lack a comprehensive understanding of these complex fluids. One key ingredient necessary for a majority of applications is the spatially and temporally resolved wall-shear stress. Besides providing a measure for the friction drag - a quantity of utmost importance in the transportation sector - it also gives insight into the dynamic loads imposed onto rigid/flexible walls, which can be crucial in human medicine. Despite its significance, it is still exceptionally difficult to measure instantaneous and spatially well-resolved wall-shear stress distributions. Most existing measurement sensors are single-direction and/or single-dimension devices that can only detect one wall-shear stress component at a fixed location. Moreover, the spatial resolution and the maximum number of jointly deployed sensors is typically limited due to experimental constraints arising from secondary electronic devices. As a result, the overwhelming majority of recent studies targeting the investigation of multi-scale phenomena that modulate the wall-shear stress dynamics are limited to time-dependent data without spatial resolution and consequently, cannot provide a comprehensive picture of the complex physics. Therefore, the overarching objective of this proposal is the development of modern deep learning based algorithms for the prediction of the wall-shear stress based on easily accessible velocity measurements. The envisioned neural networks are specifically designed to capture - without limiting assumptions - the complex non-linear and unsteady interactions that are responsible for the wall-shear stress dynamics and to make them interpretable for the human kind. In particular, this proposal targets the development of a deep learning based architecture specifically designed to learn a mapping function from two-dimensional velocity fields located in the outer layer of a turbulent wall-bounded flow to the instantaneous spatially resolved wall-shear stress distribution. Complementary, an interpretable mathematical expression, which corresponds to the inherently learnt transfer function, is extracted from the derived latent representation via symbolic regression. This expression is further investigated to gain deeper insight into the non-linear interactions that result in the modulation of the wall-shear stress. Trained on direct numerical simulation data, the generalization of the envisioned learner is evidenced based on simultaneous particle-image velocimetry measurements in the outer layer and wall-shear stress measurements using the Micro-Pillar Shear-Stress Sensor.