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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/npg-2019-61
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2019-61
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 02 Jan 2020

Submitted as: research article | 02 Jan 2020

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This preprint is currently under review for the journal NPG.

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

Ashesh Chattopadhyay1, Pedram Hassanzadeh1,2, and Devika Subramanian3,4 Ashesh Chattopadhyay et al.
  • 1Department of Mechanical Engineering, Rice University
  • 2Department of Earth Environmental and Planetary Sciences, Rice University
  • 3Department of Electrical and Computer Engineering, Rice University
  • 4Department of Computer Science, Rice University

Abstract. In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory (RNN-LSTM). This Lorenz 96 system has three tiers of nonlinearly interacting variables representing slow/large-scale (X), intermediate (Y), and fast/small-scale (Z) processes. For training or testing, only X is available; Y and Z are never known or used. We show that RC-ESN substantially outperforms ANN and RNN-LSTM for short-term prediction, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps, equivalent to several Lyapunov timescales. The RNN-LSTM and ANN show some prediction skills as well; RNN-LSTM bests ANN. Furthermore, even after losing the trajectory, data predicted by RC-ESN and RNN-LSTM have probability density functions (PDFs) that closely match the true PDF, even at the tails. The PDF of the data predicted using ANN, however, deviates from the true PDF. Implications, caveats, and applications to data-driven and data-assisted surrogate modeling of complex nonlinear dynamical systems such as weather/climate are discussed.

Ashesh Chattopadhyay et al.

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Ashesh Chattopadhyay et al.

Ashesh Chattopadhyay et al.

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Short summary
The performance of 3 deep learning methods for data-driven modeling of a multi-scale chaotic Lorenz 96 system is examined. One of the methods is found to be able to well predict the future evolution of the chaotic system from just knowing the past observations of the large scale. Potential applications to data-driven and data-assisted surrogate modeling of complex dynamical systems such as weather/climate are discussed.
The performance of 3 deep learning methods for data-driven modeling of a multi-scale chaotic...
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