Physics-Informed Echo State Networks for Chaotic Systems Forecasting

Nguyen Anh Khoa Doan*, Wolfgang Polifke, Luca Magri

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationComputational Science – ICCS 2019 - 19th International Conference, Proceedings
EditorsJoão M.F. Rodrigues, Pedro J.S. Cardoso, Jânio Monteiro, Roberto Lam, Valeria V. Krzhizhanovskaya, Michael H. Lees, Peter M.A. Sloot, Jack J. Dongarra
Number of pages7
ISBN (Print)9783030227463
Publication statusPublished - 2019
Externally publishedYes
Event19th International Conference on Computational Science, ICCS 2019 - Faro, Portugal
Duration: 12 Jun 201914 Jun 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11539 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Computational Science, ICCS 2019


  • Chaotic dynamical systems
  • Echo State Networks
  • Physics-Informed Neural Networks


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