# Physics-Informed Echo State Networks for Chaotic Systems Forecasting

arXiv: https://arxiv.org/abs/1906.11122 · HTML: https://mlsanity.com/paper/1906.11122/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.09478/) (2023)
- [Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics](https://mlsanity.com/paper/2409.01394/) (2024)
- [Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems](https://mlsanity.com/paper/2407.18057/) (2024)
- [Scope and Sense of Explainability for AI-Systems](https://mlsanity.com/paper/2112.10551/) (2021)

## Abstract (arXiv)

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapunov times as compared to conventional ESNs. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.