Learning Chaotic Dynamics using Tensor Recurrent Neural Networks

We present Tensor-RNN, a novel RNN architecture for multivariate forecasting in chaotic dynamical systems. Our proposed architecture captures highly nonlinear dynamic behavior by using high-order Markov states and transition functions. Furthermore, we decompose the highdimensional structure of the model using tensortrain networks to reduce the number of parameters while preserving the model performance. We demonstrate significant learning speed improvements over state-of-the-art RNN architectures in learning speed and predictive accuracy on a range of simulation data of non-linear dynamical systems, as well on real-world climate and traffic data. Moreover, we show that TensorRNN shows improved stable long-term forecasting for structured outputs.