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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Video prediction models based on convolutional networks, recurrent networks, and their combinations often result in blurry predictions. We identify an important contributing factor for imprecise predictions that has not been studied adequately in the literature: blind spots, i.e., lack of access to all relevant past information for accurately predicting the future. To address this issue, we introduce a fully contextaware architecture that captures the entire available past context for each pixel using Parallel Multi-Dimensional LSTM units and aggregates it using blending units. Our model outperforms a strong baseline network of 20 recurrent convolutional layers and yields state-of-the-art performance for next step prediction on three challenging real-world video datasets: Human 3.6M, Caltech Pedestrian, and UCF-101. Moreover, it does so with fewer parameters than several recently proposed models, and does not rely on deep convolutional networks, multi-scale architectures, separation of background and foreground modeling, motion flow learning, or adversarial training. These results highlight that full awareness of past context is of crucial importance for video prediction.