流体动力学在汽车、高速列车、飞行器、风力发电等多个领域中发挥着核心作用。对于流体动力学的研究而言，准确描述流场的演化特性是分析流动行为的关键。流场演化往往由一些时空相干的结构主导，这些结构在流体运动中起到决定性作用，它们的动态变化直接影响整个流场的行为，从而决定流场中工程结构的受力情况。因此，有效提取流场的关键特征对于深入理解和准确预测流体运动极为重要。通过对流场进行量化描述，我们能够更准确地揭示流场演化的主要规律，为制造业中相关产品的设计与优化提供理论支持。然而，现有的流场特征提取方法往往依赖于实验测量或数值模拟获得的高分辨率时空数据集，这在实际应用中不仅成本高昂，而且往往难以实现。因此，本文的目标是探索如何从有限的测量数据中提取流场的关键特征，以表征其流体动力学行为，并据此预测流场的演化。本文的主要研究内容和所取得的进展如下：

详细介绍神经网络与物理约束机器学习的基础原理、参数优化技术，并阐述所用到的所有验证算例所使用的数值计算方法。推导了物理信息神经网络（PINN）将物理控制方程引入神经网络的实现过程和数学表达，给出 PINN 中方程点、数据点、边界条件、初始条件的概念及其实现。这一部分的工作发展物理约束的机器学习技术，以丰富流体动力学的研究手段，并通过物理约束增强机器学习模型的可解释性。

面向风力发电场的混合数据同化，提出一种基于PINN的数据同化框架，支持使用多种类型测量数据进行训练。提出的数据同化框架以平坦地形上的大气边界层流动作为基准算例进行测试，使用风场测量中常见的各种类型数据进行训练，包括雷达视向风速、速度矢量、速度分量和压力以及它们的混合组合。经过训练的模型能够重构风力涡轮机站点上游流场的详细信息，也能够据此计算风场中的一些局部特性，如站点上游某个位置的有效风速。还引入迁移学习的策略，实现对预训练的模型的在线部署，以在线模式同化实时测量的数据，解决原始的PINN无法进行在线部署的缺陷。

为解决传统本征正交分解（POD）方法对数据质量和数量高度依赖的问题，提出一种能从稀疏测量中提取隐含的流动结构的PINN-POD方法，并在不同雷诺数下的圆柱绕流尾流中进行准确性验证。与基于高分辨率数据的传统POD方法相比，PINN-POD方法仅需少量稀疏位置观测数据即可准确捕捉流场主要特征，并展现出对测量噪声的鲁棒性。

采用傅里叶神经算子（FNO）和长短期记忆（LSTM）神经网络模型，对非定常流场演化预测进行研究。提出三种流动预测模型，分别是二维FNO直接学习并预测非定常流场、一维 FNO 和一维 LSTM 学习并预测 POD 模态时间系数。在二维圆柱绕流的非定常尾流场中进行验证，评估利用真实数据进行短时预测和利用自身预测数据迭代推演的长时预测两种模式下的预测准确性。一维FNO模型在参数量仅为二维FNO 6%的情况下，表现出最高的准确性，这表明，合适的特征提取方法和表达性更好的预测模型相结合，能够更高效准确地对非定常流场演化进行预测。

Fluid dynamics is essential across various sectors, including automotive, high-speed train, aviation, and wind power generation. The crux of fluid dynamics research lies in accurately delineating the evolution characteristics to analyze flow fields effectively. This evolution is often governed by spatiotemporal coherent structures, which are pivotal in fluid dynamics, as their dynamics significantly influence the entire flow field's evolution and, consequently, the forces exerted on engineering structures within it. Thus, the accurate extraction of key flow field features is crucial for a profound understanding and precise prediction of fluid dynamics. A quantitative description of the flow field enables a more accurate elucidation of its primary evolutionary laws, offering theoretical foundations for the design and optimization of related manufacturing products. However, traditional methods for flow field feature extraction typically rely on high-resolution spatiotemporal datasets from experimental measurements or numerical simulations. These approaches are not only expensive but also challenging to implement in real-world scenarios. Therefore, this dissertation aims to investigate methodologies for extracting crucial flow field features from limited measurement data, thereby characterizing fluid dynamics behavior and forecasting the flow field's evolution. The core research findings and advancements presented in this dissertation include:

Initially, this dissertation provides an in-depth exploration of the core principles underlying neural networks and physics-constrained machine learning, delves into parameter optimization techniques, and elaborates on the numerical simulation methods employed across various validation cases. It meticulously outlines the methodology and mathematical formulations for integrating physical governing equations into neural networks via Physics-Informed Neural Network (PINN). Furthermore, it elucidates the concepts and practical applications of equation points, data points, boundary conditions, and initial conditions within the PINN framework. This segment of the study introduces physics-constrained machine learning technologies to fluid dynamics research, improves the interpretability of machine learning models by embedding them with physical constraints.

This study develops a data assimilation framework tailored for the wind farm based on PINN and capable of being trained with a diverse array of measurement data. The efficacy of this framework is demonstrated through a benchmark case involving atmospheric boundary layer flow over flat terrain. For training, it employs commonly used wind field measurement data types, such as radar line-of-sight wind speeds, velocity vectors, velocity components, pressure, and their various combinations. The trained model is capable of reconstructing comprehensive flow field information upstream of a wind turbine site and calculating specific local wind field characteristics, like the effective wind speed at designated positions upstream. Additionally, the framework incorporates a transfer learning strategy, facilitating the online deployment of the pre-trained model for the assimilation of real-time measurement data. This addresses the limitations of original PINNs, which previously could not be deployed online.

To overcome the limitations of traditional Proper Orthogonal Decomposition (POD) methods, which rely heavily on the quality and quantity of data, a novel PINN-POD method is introduced. This innovative approach is capable of extracting implicit flow structures from sparse measurements, offering a solution to the data-dependency issue of conventional POD techniques. Its effectiveness has been rigorously tested and validated through accuracy assessments in cylinder wake flows across various Reynolds numbers. Unlike traditional POD methods that necessitate high-resolution data, the PINN-POD method achieves accurate representation of the flow field's primary features using only a minimal set of sparse observational data. Furthermore, it exhibits remarkable robustness against measurement noise.

This research delves into forecasting the evolution of unsteady flow fields through the application of Fourier Neural Operators (FNO) and Long Short-Term Memory (LSTM) models. Three distinct models were developed: a two-dimensional FNO designed to directly learn and forecast unsteady flow fields, alongside a one-dimensional FNO and a one-dimensional LSTM, both aimed at learning and predicting the temporal coefficients of POD modes. These models underwent validation within the context of unsteady wake flow fields around a two-dimensional cylinder, where their efficacy in short-term predictions using actual data and long-term forecasts using iteratively inferred data was evaluated. Remarkably, the one-dimensional FNO model, despite having only 6\% of the parameter count compared to the two-dimensional FNO, demonstrated superior accuracy. This finding underscores the potential of integrating efficient feature extraction methodologies with highly expressive predictive models to enhance the prediction of unsteady flow field evolution, both in terms of efficiency and accuracy.