Expressive Symbolic Regression for Interpretable Models of Discrete-Time Dynamical Systems
This work addresses the challenge of data-driven scientific discovery for researchers studying chaotic systems, though it appears incremental as it builds on existing SymANNTEx methods.
The authors tackled the problem of identifying interpretable mathematical expressions for discrete-time dynamical systems from data streams, using a modified SymANNTEx architecture with sparsity regularization and information theory simplification. They showed that the model properly identifies single-state maps and achieves moderate success in approximating a dual-state attractor.
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.