Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
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Author(s)
Vlachas, Pantelis R.
Byeon, Wonmin
Koumoutsakos, Petros
Wan, Zhong Yi
Sapsis, Themistoklis P.
Date Issued
May 2018
Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
Publisher
The Royal Society
Citation
Vlachas, Pantelis R., Wonmin Byeon, Zhong Y. Wan, Themistoklis P. Sapsis, and Petros Koumoutsakos. “Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 474, no. 2213 (May 2018): 20170844. © 2018 The Authors
Version
Author's final manuscript
Abstract
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long shortterm memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPS) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPS in short-Term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1098/RSPA.2017.0844
