A hybrid evolutionary algorithm for the symbolic modeling of multiple-time-scale dynamical systems

摘要

Natural and artificial dynamical systems in the real world often have dynamics at multiple time scales. Such dynamics can contribute substantially to the complexity of a dynamical system and increase the difficulty with which it can be analyzed. Although evolutionary algorithms have been proposed that are amenable to the automated modeling of dynamical systems, none have explicitly taken into account multiple time scales or leveraged the information about these dynamics that is inherent in experimental observations. We propose a hybrid approach to the design of models for multiple-time-scale dynamical systems that combines an evolutionary algorithm with other metaheuristics and conventional nonlinear regression. With only minimal human-supplied domain knowledge, the algorithm automates the process of analyzing raw experimental observations and creating an interpretable symbolic model of the system under study. We describe the algorithm in detail and demonstrate its applicability to a variety of both physical and simulated systems. In addition, we study the performance and scalability of the algorithm under different types of dynamics, varying levels of experimental noise, and other factors relevant to the practical application of the algorithm.