Many physical laws are ridge functions
Numerical Analysis
2016-05-26 v1
Abstract
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.
Cite
@article{arxiv.1605.07974,
title = {Many physical laws are ridge functions},
author = {Paul G. Constantine and Zachary del Rosario and Gianluca Iaccarino},
journal= {arXiv preprint arXiv:1605.07974},
year = {2016}
}