Dynamical system analysis of a data-driven model constructed by reservoir computing.
Dynamical system analysis of a data-driven model constructed by reservoir computing.
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DOI：
10.1103/physreve.104.044215
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发表时间：
2021-02
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影响因子：
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通讯作者：
Miki U. Kobayashi;Kengo Nakai;Yoshitaka Saiki;Natsuki Tsutsumi
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文献类型：
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作者：
Miki U. Kobayashi;Kengo Nakai;Yoshitaka Saiki;Natsuki Tsutsumi
本研究从动力系统的角度评估数据驱动模型，如不稳定不动点、周期轨道、混沌鞍、李亚普诺夫指数、流形结构和统计值。我们发现，与直接从训练数据中计算相比，数据驱动模型可以更精确地重建这些动态特性。利用这一思想，我们预测了混沌流体流动中某一宏观变量的层流持续时间分布，由于计算成本高，无法通过直接数值模拟Navier-Stokes方程来计算。
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical characteristics can be reconstructed much more precisely by a data-driven model than by computing directly from training data. With this idea, we predict the laminar lasting time distribution of a particular macroscopic variable of chaotic fluid flow, which cannot be calculated from a direct numerical simulation of the Navier-Stokes equation because of its high computational cost.