Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long-Short Term Memory Networks.

We introduce a data-driven forecasting method for high dimensional, chaoticsystems using Long-Short Term Memory (LSTM) recurrent neural networks. Theproposed LSTM neural networks perform inference of high dimensional dynamicalsystems in their reduced order space and are shown to be an effective set ofnon-linear approximators of their attractor. We demonstrate the forecastingperformance of the LSTM and compare it with Gaussian processes (GPs) in timeseries obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equationand a prototype climate model. The LSTM networks outperform the GPs inshort-term forecasting accuracy in all applications considered. A hybridarchitecture, extending the LSTM with a mean stochastic model (MSM-LSTM), isproposed to ensure convergence to the invariant measure. This novel hybridmethod is fully data-driven and extends the forecasting capabilities of LSTMnetworks.