  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
