将经典回归与物理信息结合，推动科学机器学习发展
Fundamentals of Regression
- 融合物理规律与数据驱动方法，构建物理约束的回归模型
- 提出机器学习与计算科学融合的新框架，提升模型可解释性
- 适合从事科学计算、物理建模与跨学科研究的读者
本章首先回顾了回归这一机器学习子领域的经典工具，其核心目标是发现变量间的关联关系。随着科学机器学习的发展，该领域已从纯数据驱动（统计）范式演进为受约束或“物理信息”驱动的范式，整合了物理知识与传统计算工程的方法。第一部分介绍回归的基本概念及其与其它曲线拟合方式的差异，强调其统计特性；随后概述机器学习中的传统方法，讨论其分类体系及与传统计算科学的连接路径；最后，探讨如何将机器学习与数值方法结合，以服务于物理建模与仿真。
原文摘要 · Abstract (English)
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
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