Sensitivity Analysis of a Causality-Informed Genetic Programming Ensemble for Inferring Dynamical Systems

Dynamical system is a mathematical approach to model the non-linear dynamics of complex systems over space and time. A causality-informed genetic programming (GP) ensemble methodology has been proposed recently by the authors to automatically infer dynamical systems from system observations. The method adopts a variable decomposition approach relies on expert defined causal models. However, in practice these models are bound to have inconsistencies due to human involvement. Hence, in this paper we evaluate the sensitivity of the ensemble method to the accuracy of input causal models that are used as ground truth in the formation of the ensemble. This is done by varying the accuracy of known causal models through introducing deliberate noise in models' causal relationships. Three benchmark problems are used to evaluate the performance of the proposed methodology where the output of different ensembles is compared with a standard GP algorithm. The empirical results show the effectiveness of the proposed methodology in inferring closely matching target equations under different levels of noise and learning better models than the standard GP algorithm in most cases.