Expressive Symbolic Regression for Interpretable Models of Discrete-Time Dynamical Systems

TL;DR

This paper introduces a modified SymANNTEx architecture for symbolic regression of discrete-time dynamical systems, enabling interpretable models from data with improved accuracy and simplicity, useful for scientific discovery.

Contribution

The paper presents a more expressive SymANNTEx model with optimized regression and regularization, improving identification of classical chaotic maps from data.

Findings

Successfully identifies single-state maps

Moderately approximates dual-state attractors

Shows promise for data-driven scientific discovery

Abstract

Interpretable mathematical expressions defining discrete-time dynamical systems (iterated maps) can model many phenomena of scientific interest, enabling a deeper understanding of system behaviors. Since formulating governing expressions from first principles can be difficult, it is of particular interest to identify expressions for iterated maps given only their data streams. In this work, we consider a modified Symbolic Artificial Neural Network-Trained Expressions (SymANNTEx) architecture for this task, an architecture more expressive than others in the literature. We make a modification to the model pipeline to optimize the regression, then characterize the behavior of the adjusted model in identifying several classical chaotic maps. With the goal of parsimony, sparsity-inducing weight regularization and information theory-informed simplification are implemented. We show that our modified SymANNTEx model properly identifies single-state maps and achieves moderate success in approximating a dual-state attractor. These performances offer significant promise for data-driven scientific discovery and interpretation.