Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
This addresses the computational bottleneck in design, control, and optimization for engineers and scientists, though it appears incremental as an extension of echo state networks to continuous-time stiff systems.
The paper tackles the problem of computationally expensive simulation of stiff nonlinear systems by developing continuous-time echo state networks (CTESNs) as surrogates, achieving near-constant time performance with relative error under 0.2% on a heating system model.
Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluating a cheap surrogate of the full model. Here we present a general data-driven method, the continuous-time echo state network (CTESN), for generating surrogates of nonlinear ordinary differential equations with dynamics at widely separated timescales. We empirically demonstrate near-constant time performance using our CTESNs on a physically motivated scalable model of a heating system whose full execution time increases exponentially, while maintaining relative error of within 0.2 %. We also show that our model captures fast transients as well as slow dynamics effectively, while other techniques such as physics informed neural networks have difficulties trying to train and predict the highly nonlinear behavior of these models.