水库计算数据驱动模型的动力系统分析
Dynamical system analysis of a data-driven model constructed by reservoir computing
摘要：
本研究从动力系统的角度，如不稳定不动点，周期轨道，混沌鞍，李雅普诺夫指数，流形结构和统计值的数据驱动模型进行评估。我们发现，这些动态特性可以更精确地重建数据驱动的模型，而不是直接从训练数据计算。利用这一思想，我们预测了一个特定的宏观变量的混沌流体流动的层流持续时间分布，这是不能从直接的Navier-斯托克斯方程的数值模拟计算，因为它的计算成本高.
英文摘要：
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.
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