Learning with Physical Constraints
arXiv:2512.00104v1
Originality Synthesis-oriented
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This is an incremental educational resource for learners in computational physics and machine learning.
The chapter presents tutorial exercises on physics-constrained regression for problems like super-resolution and turbulence modeling, providing Python code implementations.
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.