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Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network

A. Chattopadhyay, P. Hassanzadeh, and D. Subramanian.
Nonlinear Processes in Geophysics, 27 (3): 373-389 (2019)
DOI: https://doi.org/10.5194/npg-27-373-2020

Abstract

Abstract. In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter 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 predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) 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 and climate, are discussed.

BibTeX key: chattopadhyaydatadriven
entry type: article
year: 2019
journal: Nonlinear Processes in Geophysics
number: 3
pages: 373-389
publisher: Copernicus GmbH
volume: 27
type: misc
issn: 1023-5809
DOI: https://doi.org/10.5194/npg-27-373-2020
url: https://npg.copernicus.org/articles/27/373/2020/

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%0 Journal Article %1 chattopadhyaydatadriven %A Chattopadhyay, Ashesh %A Hassanzadeh, Pedram %A Subramanian, Devika %D 2019 %I Copernicus GmbH %J Nonlinear Processes in Geophysics %K climate climatemodeling simplemodel todo:read %N 3 %P 373-389 %R https://doi.org/10.5194/npg-27-373-2020 %T Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network %U https://npg.copernicus.org/articles/27/373/2020/ %V 27 %X Abstract. In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter 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 predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) 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 and climate, are discussed.

@article{chattopadhyaydatadriven, abstract = {Abstract. In this paper, the performance of three machine-learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multiscale spatiotemporal Lorenz 96 system is examined. The methods are an echo state network (ESN, which is a type of reservoir computing; hereafter RC–ESN), a deep feed-forward artificial neural network (ANN), and a recurrent neural network (RNN) with long short-term memory (LSTM; hereafter 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 predictions, e.g., accurately forecasting the chaotic trajectories for hundreds of numerical solver's time steps equivalent to several Lyapunov timescales. The RNN–LSTM outperforms ANN, and both methods show some prediction skills too. Furthermore, even after losing the trajectory, data predicted by RC–ESN and RNN–LSTM have probability density functions (pdf's) 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 and climate, are discussed.}, added-at = {2022-03-31T13:29:22.000+0200}, author = {Chattopadhyay, Ashesh and Hassanzadeh, Pedram and Subramanian, Devika}, biburl = {https://www.bibsonomy.org/bibtex/2bf3d53b0abaae83e070651a17db66426/annakrause}, description = {NPG - Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network}, doi = {https://doi.org/10.5194/npg-27-373-2020}, interhash = {7e8c1d50841fbcb930efd6f96c709bba}, intrahash = {bf3d53b0abaae83e070651a17db66426}, issn = {1023-5809}, journal = {Nonlinear Processes in Geophysics}, keywords = {climate climatemodeling simplemodel todo:read}, number = 3, pages = {373-389}, publisher = {Copernicus GmbH}, timestamp = {2022-03-31T13:30:26.000+0200}, title = {Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network}, type = {misc}, url = {https://npg.copernicus.org/articles/27/373/2020/}, volume = 27, year = 2019 }

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Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network

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