# Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks

arXiv: https://arxiv.org/abs/2010.04004 · HTML: https://mlsanity.com/paper/2010.04004/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators](https://mlsanity.com/paper/2301.12538/) (2023)
- [ReservoirComputing.jl: An Efficient and Modular Library for Reservoir Computing Models](https://mlsanity.com/paper/2204.05117/) (2022)
- [Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!](https://mlsanity.com/paper/2303.02262/) (2023)
- [A Meta-learning Approach to Reservoir Computing: Time Series Prediction with Limited Data](https://mlsanity.com/paper/2110.03722/) (2021)
- [LiLaN: A Linear Latent Network as the Solution Operator for Real-Time Solutions to Stiff Nonlinear Ordinary Differential Equations](https://mlsanity.com/paper/2501.08423/) (2025)

## Abstract (arXiv)

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.