Identifing the structure of dynamical multivariate complex systems and its visualization and application for optimization engineering

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Real systems are often composed by many elements interacting with each other and show us complex behavior. To predict these complex systems, we can refer to their past behavior, but all of the observed elements do not always compose the same system. Thus, we have to detect some essential elements from the observed elements so as to improve the prediction accuracy of learning data. Moreover, if we apply Takens's embedding theorem to reconstruct an attractor only by single element, we don't have to select elements, but we have to optimize embedding parameters. In any case, because we have to solve above optimization problems, we applied the genetic algorithm (GA) as one of the meta-heuristic techniques. Moreover, real systems might be nonstationary and their own mechanism changes dynamically. Therefore, we reiterated the GA for each optimization with simple algorithms to embed and to predict time-series data for saving numerical costs. Through some simulations, we confirmed that our dynamical optimization can improve prediction accuracy of multivariate nonlinear systems, even financial markets, and can help us to examine whether the structure of a complex system dynamically changes or not.