Modeling hierarchy using symbolic regression

Symbolic regression (SR) is an attractive modeling approach because it can capture and present, mathematically, relationships between variables of interest. However, given n variables to model, symbolic regression returns a flat list of n equations. As the number of state variables to be modeled scales, interpretation of such a list becomes difficult. Here we present a symbolic regression method that detects and captures hidden hierarchy in a given system. The method returns the equations in a hierarchical dependency graph, which increases the interpretability of the results. We demonstrate that two variations of this hierarchical modeling approach outperform non-hierarchical symbolic regression on a synthetic data suite.