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

真实的系统往往是由许多相互作用的元素组成的，表现出复杂的行为。为了预测这些复杂系统，我们可以参考它们过去的行为，但所有观察到的元素并不总是组成同一个系统。因此，我们必须从观察到的元素中检测出一些基本元素，以提高学习数据的预测精度。此外，如果我们应用Takens的嵌入定理，仅由单个元素来重构吸引子，我们不必选择元素，但我们必须优化嵌入参数。在任何情况下，因为我们必须解决上述优化问题，我们应用遗传算法（GA）作为元启发式技术之一。此外，真实的系统可能是非平稳的，并且它们自身的机制是动态变化的。因此，我们用简单的算法重复了每个优化的GA，以嵌入和预测时间序列数据，以节省数值成本。通过一些仿真实验，我们证实了我们的动态优化可以提高多元非线性系统甚至金融市场的预测精度，并且可以帮助我们检验复杂系统的结构是否动态变化。

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.