Many physical laws are ridge functions
For physicists and applied mathematicians, it provides a theoretical foundation linking physical laws to ridge functions and subspace methods, though the insight is largely conceptual.
The paper demonstrates that many physical laws are ridge functions, using dimensional analysis to reveal their structure and connecting this to modern dimension reduction techniques like active subspaces and sufficient dimension reduction.
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.