Fundamentals of Regression
Abstract
This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics
Cite
@article{arxiv.2512.01920,
title = {Fundamentals of Regression},
author = {Miguel A. Mendez},
journal= {arXiv preprint arXiv:2512.01920},
year = {2025}
}
Comments
Chapter 2 from Machine Learning for Fluid Dynamics (ISBN 978-2875162090). Based on the VKI-ULB lecture series ''Machine Learning for Fluid Dynamics,'' held in Brussels in February 2022