Learning Wave Propagation with Attention-Based Convolutional Recurrent Autoencoder Net

In this paper, we present an end-to-end attention-based convolutional recurrent autoencoder (AB-CRAN) network for data-driven modeling of wave propagation phenomena. The proposed network architecture relies on the attention-based recurrent neural network (RNN) with long short-term memory (LSTM) cells. To construct the low-dimensional learning model, we employ a denoising-based convolutional autoencoder from the full-order snapshots given by time-dependent hyperbolic partial differential equations for wave propagation. To begin, we attempt to address the difficulty in evolving the low-dimensional representation in time with a plain RNN-LSTM for wave propagation phenomenon. We build an attention-based sequence-to-sequence RNN-LSTM architecture to predict the solution over a long time horizon. To demonstrate the effectiveness of the proposed learning model, we consider three benchmark problems namely one-dimensional linear convection, nonlinear viscous Burgers, and two-dimensional Saint-Venant shallow water system. Using the time-series datasets from the benchmark problems, our novel AB-CRAN architecture accurately captures the wave amplitude and preserves the wave characteristics of the solution for long time horizons. The attention-based sequence-to-sequence network increases the time-horizon of prediction by five times compared to the plain RNN-LSTM. Denoising autoencoder further reduces the mean squared error of prediction and improves the generalization capability in the parameter space.