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Surrogates for Stiff Nonlinear Systems using Continuous Time Echo State Networks
Ranjan Anantharaman · Christopher Rackauckas · Viral Shah

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.

Author Information

Ranjan Anantharaman (MIT)
Christopher Rackauckas (Massachusetts Institute of Technology)

I am a mathematician and pharmacologist at MIT and the University of Maryland, School of Pharmacy. My programming language of choice is Julia. I run a [blog on Julia, mathematics, and stochastic biology](http://www.stochasticlifestyle.com/) and I have developed a few libraries in Julia, including (but not limited to) [DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl) and [Pumas](https://pumas.ai/). For more information, please check out my [Github profile](https://github.com/ChrisRackauckas) or my [personal website](http://chrisrackauckas.com/).

Viral Shah (Julia Computing, Inc.)

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