基于李雅普诺夫函数的油藏计算机动态稳定性分析
Stability Analysis of Reservoir Computers Dynamics via Lyapunov Functions
摘要：
一个李雅普诺夫设计方法是用来分析一个通用的水库计算机的连续时间和离散时间动态的情况下的非线性稳定性。使用这种方法，对于一个给定的非线性油藏计算机，一个固定点周围的径向稳定区域的解析确定。我们看到，在分析预测全局稳定性的区域中，水库计算机的训练误差较低，但也受到水库系统的个体动态的特定选择的影响。对于动态是多项式的情况，多项式具有对应于至少一个奇次幂的非零系数（例如，线性项）和一个偶次幂（例如，二次项）。
英文摘要：
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial region of stability around a fixed point is analytically determined. We see that the training error of the reservoir computer is lower in the region where the analysis predicts global stability but is also affected by the particular choice of the individual dynamics for the reservoir systems. For the case that the dynamics is polynomial, it appears to be important for the polynomial to have nonzero coefficients corresponding to at least one odd power (e.g., linear term) and one even power (e.g., quadratic term).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
