Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the generalization accuracy of a CTESN surrogate is the method of projecting the reservoir state to the output. This paper shows that of the two common projection methods (linear and nonlinear), the surrogates developed via the nonlinear projection consistently outperform those developed via the linear method. CTESN surrogates are developed for several challenging benchmark cases governed by stiff ODEs, and for each case, the performance of the linear and nonlinear projections is compared. The results of this paper demonstrate the applicability of CTESNs to a variety of problems while serving as a reference for important algorithmic and hyper-parameter choices for CTESNs

翻译：连续时间回声状态网络（CTESNs）是一种有前景但尚未充分探索的代理建模技术，尤其适用于由刚性常微分方程（ODEs）控制的动力学系统。影响CTESN代理泛化精度的关键因素在于将储备池状态投影到输出的方法。本文表明，在两种常见投影方法（线性和非线性）中，通过非线性投影开发的代理始终优于线性方法。针对多个由刚性ODEs控制的具有挑战性的基准案例，本文开发了CTESN代理，并对每种案例下的线性和非线性投影性能进行了比较。本文结果证明了CTESNs在多种问题上的适用性，同时为CTESNs的重要算法和超参数选择提供了参考。