{"ID":2835856,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00104","arxiv_id":"2512.00104","title":"Learning with Physical Constraints","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.","short_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...","url_abs":"https://arxiv.org/abs/2512.00104","url_pdf":"https://arxiv.org/pdf/2512.00104v1","authors":"[\"Miguel A. Mendez\",\"Jan van Den Berghe\",\"Manuel Ratz\",\"Matilde Fiore\",\"Lorenzo Schena\"]","published":"2025-11-27T08:50:18Z","proceeding":"physics.flu-dyn","tasks":"[\"physics.flu-dyn\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}