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

arXiv: https://arxiv.org/abs/2406.06585 · HTML: https://mlsanity.com/paper/2406.06585/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)

## Built on by (most cited first, 1 of 1)

- [Symbolic Neural ODEs: Learning interpretable models from time-series data](https://mlsanity.com/paper/2608.22112/) (2026)

## Abstract (arXiv)

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.