Dynamical Kinds and their Discovery

TL;DR

This paper introduces an algorithm that classifies causal systems into dynamical kinds based on shared symmetries, without requiring explicit models or prior knowledge, aiding scientific discovery.

Contribution

It presents the first algorithm for classifying dynamical systems into kinds using symmetry comparisons, robust to noise and sampling errors.

Findings

Successfully classifies nonlinear systems into dynamical kinds

Robust classification despite noisy and limited data

Fails gracefully when systems are highly similar

Abstract

We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to determine whether arbitrary systems are governed by causal relations of the same form offers significant practical applications in the development and validation of dynamical models. It is also of theoretical interest as an essential stage in the scientific inference of laws from empirical data. The algorithm presented is based on the dynamical symmetry approach to dynamical kinds. A dynamical symmetry with respect to time is an intervention on one or more variables of a system that commutes with the time evolution of the system. A dynamical kind is a class of systems sharing a set of dynamical symmetries. The algorithm presented classifies deterministic, time-dependent causal systems by directly comparing their exhibited symmetries. Using simulated, noisy data from a variety of nonlinear systems, we show that this algorithm correctly sorts systems into dynamical kinds. It is robust under significant sampling error, is immune to violations of normality in sampling error, and fails gracefully with increasing dynamical similarity. The algorithm we demonstrate is the first to address this aspect of automated scientific discovery.