Dimensional Reduction of Dynamical Systems by Machine Learning: Automatic Generation of the Optimum Extensive Variables and Their Time-Evolution Map

TL;DR

This paper introduces a machine learning framework that automatically identifies optimal macroscopic variables and their evolution rules from complex dynamical systems, demonstrated on the three-state Potts model.

Contribution

It presents a novel method for dimensional reduction of dynamical systems by simultaneously discovering extensive variables and their dynamics using machine learning.

Findings

Successfully applied to the three-state Potts model

Automatically generates effective macroscopic variables

Accurately captures the system's time evolution

Abstract

A framework is proposed to generate a phenomenological model that extracts the essence of a dynamical system (DS) with large degrees of freedom using machine learning. For a given microscopic DS, the optimum transformation to a small number of macroscopic variables, which is expected to be extensive, and the rule of time evolution that the variables obey are simultaneously identified. The utility of this method is demonstrated through its application to the nonequilibrium relaxation of the three-state Potts model.