Continuous Time Echo State Networks (CTESN) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). This paper critically investigates the effects of important hyper-parameters and algorithmic choices on the generalization capability of CTESN surrogates on two benchmark problems governed by Robertson's equations. The method is also used to parametrize the initial conditions of a system of ODEs that realistically model automobile collisions, solving them accurately up to 200 times faster than numerical ODE solvers. The results of this paper demonstrate the ability of CTESN surrogates to accurately predict sharp transients and highly nonlinear system responses, and their utility in speeding up the solution of stiff ODE systems, allowing for their use in diverse applications from accelerated design optimization to digital twins.

翻译：连续时间回声状态网络（CTESN）是一种有前景但尚未充分探索的动态系统代理建模技术，尤其适用于由刚性常微分方程主导的系统。本文以罗伯逊方程为基准，通过两个基准问题系统研究了关键超参数和算法选择对CTESN代理泛化能力的影响。该方法还被用于对真实模拟汽车碰撞的常微分方程组系统进行初始条件参数化，其求解速度比数值常微分方程求解器快达200倍。研究结果表明，CTESN代理能够准确预测陡峭瞬态响应和高度非线性系统行为，在加速刚性常微分方程求解方面具有实用价值，可广泛应用于从加速设计优化到数字孪生等多样化场景。