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.

通过对修正的SymANNTEx模型进行权重正则化和信息论简化，本研究在识别经典混沌映射中成功识别单状态映射，并在逼近双状态吸引子方面取得了适度的成果，这为基于数据的科学发现和解释提供了重要的前景。

离散时间动力系统的可解释模型的表达式符号回归