Many physical laws are ridge functions
Many physical laws are ridge functions
复制标题
许多物理定律都是岭函数
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. Iaccarino
中科院分区：
文献类型：
--
作者：
P. Constantine;Z. Rosario;G. Iaccarino
岭函数是多个变量的函数，该函数在其域中沿某些方向保持不变。使用经典的量纲分析，我们证明许多物理定律都是岭函数；这一事实使我们能够深入了解物理定律的结构，并激发对岭函数及其特性的进一步研究。我们还将维度分析与现代基于子空间的降维技术联系起来，包括确定性近似中的活动子空间和统计回归中的充分降维。
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws are ridge functions; this fact yields insight into the structure of physical laws and motivates further study into ridge functions and their properties. We also connect dimensional analysis to modern subspace-based techniques for dimension reduction, including active subspaces in deterministic approximation and sufficient dimension reduction in statistical regression.