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Physics-Informed Echo State Networks for Chaotic Systems Forecasting

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11539)


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.


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

The authors acknowledge the support of the Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no. 291763. L.M. also acknowledges the Royal Academy of Engineering Research Fellowship Scheme.

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Correspondence to Nguyen Anh Khoa Doan .

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Doan, N.A.K., Polifke, W., Magri, L. (2019). Physics-Informed Echo State Networks for Chaotic Systems Forecasting. In: , et al. Computational Science – ICCS 2019. ICCS 2019. Lecture Notes in Computer Science(), vol 11539. Springer, Cham.

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