Inference of compact nonlinear dynamic models by epigenetic local search

We introduce a method to enhance the inference of meaningful dynamic models from observational data by genetic programming (GP). This method incorporates an inheritable epigenetic layer that specifies active and inactive genes for a more effective local search of the model structure space. We define several GP implementations using different features of epigenetics, such as passive structure, phenotypic plasticity, and inheritable gene regulation. To test these implementations, we use hundreds of data sets generated from nonlinear ordinary differential equations (ODEs) in several fields of engineering and from randomly constructed nonlinear ODE models. The results indicate that epigenetic hill climbing consistently produces more compact dynamic equations with better fitness values, and that it identifies the exact solution of the system more often, validating the categorical improvement of GP by epigenetic local search. The results further indicate that when faced with complex dynamics, epigenetic hill climbing reduces the computational effort required to infer the correct underlying dynamics. We then apply the method to the identification of three real-world systems: a cascaded tanks system, a chemical distillation tower, and an industrial wind turbine. We analyze its solutions in comparison to theoretical and black-box approaches in terms of accuracy and intelligibility. Finally, we analyze population homology to evaluate the efficiency of the method. The results indicate that the epigenetic implementations provide protection from premature convergence by maintaining diversity in silenced portions of programs.