Automatic Derivation of Nonlinear State Equations by Using Artificial Intelligence in Inverse Problem of Complex Systems

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Estimation of the interaction mechanisms among system components by using experimentally observed dynamic responses (time-courses) of some of the system components is generally referred to as "inverse problem". Especially in complex systems such as chaos, only a slight difference in interaction mechanism or in initial value of a system component causes a drastic change in time-course responses of system components.In this study, given experimentally observed time series data of system components, we have developed the inference system of interaction mechanism among system components based on evolutional algorithm (genetic programming, genetic algorithm). This system allows an automatic derivation of simultaneous differential equations based on generalized mass action law (GMA) which realize the experimentally observed time course data of system components. We have performed the validation of this sytem in the cases of two and three dimensional simultaneous nonlinear differential equations.