Predicting waves in fluids with deep neural network

TL;DR

This paper introduces an attention-based convolutional recurrent autoencoder network (AB-CRAN) for data-driven wave prediction in fluids, demonstrating improved accuracy and longer prediction horizons over standard RNNs across multiple benchmark problems.

Contribution

The paper develops a novel AB-CRAN architecture combining attention mechanisms and autoencoders for improved wave prediction in fluid dynamics.

Findings

AB-CRAN accurately captures wave amplitude and characteristics over long time horizons.

Attention mechanisms extend the prediction horizon compared to standard RNNs.

Denoising autoencoder reduces prediction error and enhances generalization.

Abstract

In this paper, we present a deep learning technique for data-driven predictions of wave propagation in a fluid medium. The technique relies on an attention-based convolutional recurrent autoencoder network (AB-CRAN). To construct a low-dimensional representation of wave propagation data, we employ a denoising-based convolutional autoencoder. The AB-CRAN architecture with attention-based long short-term memory cells forms our deep neural network model for the time marching of the low-dimensional features. We assess the proposed AB-CRAN framework against the standard recurrent neural network for the low-dimensional learning of wave propagation. To demonstrate the effectiveness of the AB-CRAN model, we consider three benchmark problems, namely, one-dimensional linear convection, the nonlinear viscous Burgers equation, and the two-dimensional Saint-Venant shallow water system. Using the spatial-temporal 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 compared to the standard recurrent neural network with long short-term memory cells. The denoising autoencoder further reduces the mean squared error of prediction and improves the generalization capability in the parameter space.