# Predicting waves in fluids with deep neural network

arXiv: https://arxiv.org/abs/2201.06628 · HTML: https://mlsanity.com/paper/2201.06628/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [From Principal Subspaces to Principal Components with Linear Autoencoders](https://mlsanity.com/paper/1804.10253/) (2018)
- [Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks](https://mlsanity.com/paper/1807.02901/) (2018)
- [Assessment of unsteady flow predictions using hybrid deep learning based reduced order models](https://mlsanity.com/paper/2009.04396/) (2020)
- [Approximating the solution to wave propagation using deep neural networks](https://mlsanity.com/paper/1812.01609/) (2018)
- [Kolmogorov n-widths for linear dynamical systems](https://mlsanity.com/paper/1806.09880/) (2018)
- [Physics-aware registration based auto-encoder for convection dominated PDEs](https://mlsanity.com/paper/2006.15655/) (2020)

## Built on by (most cited first, 7 of 7)

- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [Continual Learning of Range-Dependent Transmission Loss for Underwater Acoustic using Conditional Convolutional Neural Net](https://mlsanity.com/paper/2404.08091/) (2024)
- [Harnessing Loss Decomposition for Long-Horizon Wave Predictions via Deep Neural Networks](https://mlsanity.com/paper/2412.02924/) (2024)
- [Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decomposition](https://mlsanity.com/paper/2504.11433/) (2025)
- [Assessment of convolutional recurrent autoencoder network for learning wave propagation](https://mlsanity.com/paper/2204.05573/) (2022)
- [Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics](https://mlsanity.com/paper/2211.00307/) (2022)
- [A Physics-Guided Probabilistic Surrogate Modeling Framework for Digital Twins of Underwater Radiated Noise](https://mlsanity.com/paper/2509.25730/) (2025)

## Abstract (arXiv)

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.