Data driven governing equations approximations using attention based multistep neural networks

During the past decade, deep learning has represented the biggest research trend in the field of machine learning, which provides new powerful tools to interrogate high dimensional time series data in a way that has not been possible before. With the recent success in natural language processing, one would expect widespread adaptation to problems like time series forecasting and classification. After all, both involve processing sequential data. However, to this point, research on their adaptation to time series problems has remained limited. Recently, a multi-step time-stepping scheme without the need of direct access to temporal gradients has been proposed, which can accurately identify nonlinear dynamical systems from time series data. In this paper, we combined an attention mechanism with a deep model in a multi-step time-stepping scheme to perform nonlinear system identification and forecasting tasks. To our knowledge, this is the first paper to use attention based models to deal with nonlinear system identification and forecasting problems. The attention weights on rows select those variables that are helpful for forecasting, which can enhance the information across multiple time steps to capture temporal information. The experiment results indicate that the attention based model in a multi-step time-stepping scheme has better identification and prediction performance for nonlinear time series identification and forecasting problems.