[arxiv]  [paper]

Abstract

We introduce a data-driven forecasting method forhigh-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. Theproposed LSTM neural networks perform inference ofhigh-dimensional dynamical systems in their reducedorder space and are shown to be an effectiveset 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 Lorenz96 system, the Kuramoto–Sivashinsky equation and a prototype climate model. The LSTM networksoutperform the GPs in short-term forecasting accuracyin all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model(MSM–LSTM), is proposed to ensure convergence tothe invariant measure. This novel hybrid methodis fully data-driven and extends the forecastingcapabilities of LSTM networks.

@article {Vlachas20170844,
	author = {Vlachas, Pantelis R. and Byeon, Wonmin and Wan, Zhong Y. and Sapsis, Themistoklis P. and Koumoutsakos, Petros},
	title = {Data-driven Forecasting of High-dimensional Chaotic Systems with Long Short-Term Memory Networks},
	volume = {474},
	number = {2213},
	year = {2018},
	doi = {10.1098/rspa.2017.0844},
	publisher = {The Royal Society},
	issn = {1364-5021},
	URL = {http://rspa.royalsocietypublishing.org/content/474/2213/20170844},
	eprint = {http://rspa.royalsocietypublishing.org/content/474/2213/20170844.full.pdf},
	journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}