Inference of differential equations by using genetic programming

Abstract

The ordinary differential equations (ODEs) are used as a mathematical method for the sake of modeling a complicated nonlinear system. This approach is well-known to be useful for the practical application, e.g., bioinformatics, chemical reaction models, controlling theory etc. In this paper, we propose a new evolutionary method by which to make inference of a system of ODEs. To explore the search space more effectively in the course of evolution, the right-hand sides of ODEs are inferred by Genetic Programming (GP) and the least mean square (LMS) method is used along with the ordinary GP. We apply our method to several target tasks and empirically show how successfully GP infers the systems of ODEs. We also describe how our approach is extended to solve the inference of a differential equation system including transdential functions. Copyright © 2004 JSAI.