Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems

TL;DR

This paper introduces a deep learning framework combining convolutional autoencoders and LSTM networks for efficient, non-intrusive model reduction of high-dimensional fluid systems, enabling accurate long-term predictions.

Contribution

It proposes a novel modular deep learning approach for nonlinear model reduction that does not require access to system operators and effectively captures complex fluid dynamics.

Findings

Accurately predicts fluid system behavior with large parameter variations.

Demonstrates stability in long-term fluid flow predictions.

Outperforms traditional projection-based methods in efficiency and accuracy.

Abstract

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing equations onto a subspace spanned by basis functions obtained from the compression of a dataset of solution snapshots. However, this method is intrusive since the projection requires access to the system operators. Further, some systems may require special treatment of nonlinearities to ensure computational efficiency or additional modeling to preserve stability. In this work we propose a deep learning-based strategy for nonlinear model reduction that is inspired by projection-based model reduction where the idea is to identify some optimal low-dimensional representation and evolve it in time. Our approach constructs a modular model consisting of a deep convolutional autoencoder and a modified LSTM network. The deep convolutional autoencoder returns a low-dimensional representation in terms of coordinates on some expressive nonlinear data-supporting manifold. The dynamics on this manifold are then modeled by the modified LSTM network in a computationally efficient manner. An offline unsupervised training strategy that exploits the model modularity is also developed. We demonstrate our model on three illustrative examples each highlighting the model's performance in prediction tasks for fluid systems with large parameter-variations and its stability in long-term prediction.