Inference of differential equation models by genetic programming

This paper describes an evolutionary method for identifying a causal model from the observed time series data. We use a system of ordinary differential equations (ODEs) as the causal model. This approach is well-known to be useful for the practical application, e.g., bioinformatics, chemical reaction models, controlling theory etc. 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.