An Information Theory Approach to Physical Domain Discovery

TL;DR

This paper presents an information-theoretic method for discovering physical domains by minimizing description entropy, effectively identifying different physical regions in complex systems through recursive partitioning.

Contribution

It introduces a novel recursive domain partitioning method that optimizes physical descriptions by entropy minimization, applicable to complex systems.

Findings

Successfully identified elastic and plastic regions in stress-strain data

Discovered flow regions in fluid simulations

Demonstrated effectiveness in 1D and 2D physical systems

Abstract

The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both predictive error on the dataset and the complexity of the description. The discovery of the governing physics of a system can therefore be viewed as a mathematical optimization problem. We outline here a method to optimize the description of arbitrarily complex physical systems by minimizing the entropy of the description of the system. The Recursive Domain Partitioning (RDP) procedure finds the optimum partitioning of each physical domain into subdomains, and the optimum predictive function within each subdomain. Penalty functions are introduced to limit the complexity of the predictive function within each domain. Examples are shown in 1D and 2D. In 1D, the technique effectively discovers the elastic and plastic regions within a stress-strain curve generated by simulations of amorphous carbon material, while in 2D the technique discovers the free-flow region and the inertially-obstructed flow region in the simulation of fluid flow across a plate.