# Assessment of convolutional recurrent autoencoder network for learning wave propagation

arXiv: https://arxiv.org/abs/2204.05573 · HTML: https://mlsanity.com/paper/2204.05573/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (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)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [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)
- [Assessment of unsteady flow predictions using hybrid deep learning based reduced order models](https://mlsanity.com/paper/2009.04396/) (2020)
- [Comparing recurrent and convolutional neural networks for predicting wave propagation](https://mlsanity.com/paper/2002.08981/) (2020)
- [Predicting waves in fluids with deep neural network](https://mlsanity.com/paper/2201.06628/) (2022)

## Abstract (arXiv)

It is challenging to construct generalized physical models of wave propagation in nature owing to their complex physics as well as widely varying environmental parameters and dynamical scales. In this article, we present the convolutional autoencoder recurrent network (CRAN) as a data-driven model for learning wave propagation phenomena. The CRAN consists of a convolutional autoencoder for learning low-dimensional system representation and a long short-term memory recurrent neural network for the system evolution in low dimension. We show that the convolutional autoencoder significantly outperforms the dimension-reduction of complex wave propagation phenomena via projection-based methods as it can directly learn subspaces resembling wave characteristics. On the other hand, the projection-based modes are restricted to the Fourier subspace. Geometric priors of the convolutional autoencoder enabling selective scale separation of complex wave dynamics further enhance its dimension-reduction capability. We also demonstrate that geometric priors such as translation equivariance and translational invariance of the convolutional autoencoder enable generalized learning of low-dimensional maps. Thus, the composite CRAN model connecting the convolutional autoencoder with a long short-term memory network specially designed for autoregressive modeling can perform generalized wave propagation prediction over the desired time horizon. Numerical experiments display 90% mean structural similarity index measure of CRAN predictions compared to true solutions for out-of-training cases, and less than 10% pointwise L1 error for most cases, verifying such generalization claims. Finally, the CRAN predictions offer similar wave characteristic patterns to the target solutions indicating not only their generalization but also their kinematical consistency.