# Learning with Physical Constraints

arXiv: https://arxiv.org/abs/2512.00104 · HTML: https://mlsanity.com/paper/2512.00104/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2025.

## Abstract (arXiv)

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.