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。