Parameter Space Compression Underlies Emergent Theories and Predictive Models

TL;DR

This paper demonstrates that the emergence of simplified, predictive models across sciences is due to a hierarchy of parameter importance, which compresses microscopic details into a few key parameters.

Contribution

It explicitly links parameter space compression in physics to similar phenomena in other scientific models using Fisher Information Matrix analysis.

Findings

Hierarchy of parameter importance is universal across models.

Effective models emerge from parameter space compression.

Predictive power persists despite microscopic uncertainties.

Abstract

We report a similarity between the microscopic parameter dependance of emergent theories in physics and that of multiparameter models common in other areas of science. In both cases, predictions are possible despite large uncertainties in the microscopic parameters because these details are compressed into just a few governing parameters that are sufficient to describe relevant observables. We make this commonality explicit by examining parameter sensitivity in a hopping model of diffusion and a generalized Ising model of ferromagnetism. We trace the emergence of a smaller effective model to the development of a hierarchy of parameter importance quantified by the eigenvalues of the Fisher Information Matrix. Strikingly, the same hierarchy appears ubiquitously in models taken from diverse areas of science. We conclude that the emergence of effective continuum and universal theories in physics is due to the same parameter space hierarchy that underlies predictive modeling in other areas of science.