Learning with Physical Constraints

TL;DR

This paper presents three tutorial exercises on physics-constrained regression, demonstrating applications in velocity field super-resolution, turbulence modeling, and system identification, with accompanying Python code.

Contribution

It introduces practical toy problems for physics-constrained regression, illustrating its use in complex physical systems and providing accessible code implementations.

Findings

Demonstrated physics-constrained regression for velocity super-resolution

Applied data-driven methods to turbulence modeling

Showcased system identification for forecasting and control

Abstract

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.