🤖 AI Summary
This paper addresses three physics-constrained regression problems in fluid mechanics: PIV velocity field super-resolution and data assimilation, data-driven turbulence modeling, and system identification for digital twin predictive control. Methodologically, it proposes a physics-informed regression framework that incorporates conservation laws—such as the Navier–Stokes equations—as soft constraints into supervised learning objectives; gradient-based optimization is enabled via automatic differentiation, and differentiable physics-informed models are implemented in Python. Key contributions include: (1) a unified approach to modeling under multiscale dynamics, limited data, and high noise; (2) substantially improved model generalizability and physical consistency; and (3) publicly available, reproducible educational case studies and code, demonstrating the efficacy and pedagogical versatility of physics-informed learning in scientific discovery and engineering closed-loop 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.