Investigating the Surrogate Modeling Capabilities of Continuous Time Echo State Networks

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.