This chapter provides three tutorial exercises on physics-constrained regression. These are implemented as toy problems that seek to mimic grand challenges in (1) the super-resolution and data assimilation of the velocity field in image velocimetry, (2) data-driven turbulence modeling, and (3) system identification and digital twinning for forecasting and control. The Python codes for all exercises are provided in the course repository.

翻译：本章提供了三个关于物理约束回归的教程练习。这些练习以玩具问题的形式实现，旨在模拟以下重大挑战：(1) 图像测速中速度场的超分辨率与数据同化，(2) 数据驱动的湍流建模，以及 (3) 用于预测与控制的系统辨识与数字孪生。所有练习的Python代码均已在课程仓库中提供。