Synchronization of chaotic systems and long short-term memory networks by sharing a single variable

We adopt long short-term memory (LSTM) networks to model and characterize chaotic systems rather than conventional dynamical equations. We find that a well-trained LSTM system can synchronize with its learned chaotic system via transmitting a common signal. In the same fashion, we show that when learning an identical chaotic system, the trained LSTM systems can also be synchronized. Remarkably, we find that a cascading synchronization will be achieved among chaotic systems and their trained LSTM systems in the same manner. We further validate that this synchronization behavior is robust even the transmitting signal is contaminated with relatively a high level of white noise. Our work reveals that synchronization is a common behavior linking chaotic systems and their learned LSTM networks.

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A Short-Term Wind Speed Forecasting Model Based on a Multi-Variable Long Short-Term Memory Network

Atmosphere ◽

10.3390/atmos12050651 ◽

2021 ◽

Vol 12 (5) ◽

pp. 651

Author(s):

Anqi Xie ◽

Hao Yang ◽

Jing Chen ◽

Li Sheng ◽

Qian Zhang

Keyword(s):

Wind Speed ◽

Short Term Memory ◽

Mean Bias Error ◽

Single Variable ◽

Short Term ◽

Term Memory ◽

Wind Speed Forecasting ◽

Memory Network ◽

Test Sets ◽

Long Short Term Memory

Accurately forecasting wind speed on a short-term scale has become essential in the field of wind power energy. In this paper, a multi-variable long short-term memory network model (MV-LSTM) based on Pearson correlation coefficient feature selection is proposed to predict the short-term wind speed. The proposed method utilizes multiple historical meteorological variables, such as wind speed, temperature, humidity, and air pressure, to predict the wind speed in the next hour. Hourly data collected from two ground observation stations in Yanqing and Zhaitang in Beijing were divided into training and test sets. The training sets were used to train the model, and the test sets were used to evaluate the model with the root-mean-square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and mean absolute percentage error (MAPE) metrics. The proposed method is compared with two other forecasting methods (the autoregressive moving average model (ARMA) method and the single-variable long short-term memory network (LSTM) method, which inputs only historical wind speed data) based on the same dataset. The experimental results prove the feasibility of the MV-LSTM method for short-term wind speed forecasting and its superiority to the ARMA method and the single-variable LSTM method.

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Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0844 ◽

2018 ◽

Vol 474 (2213) ◽

pp. 20170844 ◽

Cited By ~ 77

Author(s):

Pantelis R. Vlachas ◽

Wonmin Byeon ◽

Zhong Y. Wan ◽

Themistoklis P. Sapsis ◽

Petros Koumoutsakos

Keyword(s):

Neural Networks ◽

Chaotic Systems ◽

Climate Model ◽

Short Term Memory ◽

Data Driven ◽

High Dimensional ◽

Hybrid Architecture ◽

Short Term ◽

Term Memory ◽

Long Short Term Memory

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term 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.

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