Abstract
This paper builds on advancements in the field of Computational Intelligence to develop a robust approach that combines stochastic optimization methods utilizing Genetic Programming, together with nonlinear evolutionary optimization methods for optimizing the parameters, and Computer Algebra techniques that involve symbolic manipulation of expressions during the course of evolution, to “discover” a parsimonious differential operator that represents an optimum match to the governing differential equation of the target complex nonlinear system and subsequently discloses the correct nature of the investigated system. The proposed scheme requires input and output data only, without postulating any model class in advance. This technique can also discover an accurate single expression, with direct physical interpretation, that represents the governing multi-region (response domain) equations of systems that incorporate certain classes of nonlinear phenomena (such as yielding). Yet, unlike many conventional nonparametric techniques whose approximations result in undesirable oscillations around unsmooth points, automatic incorporation of discontinuous basis functions in this approach eliminates the need of such approximations and their concomitant errors. A variety of highly nonlinear phenomena are considered to assess the capabilities and the generalization extent of the suggested approach. It is shown that the method of this paper provides a robust methodology for developing reduced-order, reduced-complexity, computational models (in the form of governing differential equations) that can be used for obtaining high-fidelity models that reflect the correct “physics” of the underlying phenomena.