Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows

TL;DR

This paper introduces a deep learning-based reduced order modeling approach for unsteady fluid flows, utilizing autoencoders for nonlinear feature extraction and LSTM networks for future state prediction, outperforming traditional methods.

Contribution

The paper presents a novel autoencoder-LSTM framework for nonlinear reduced order modeling of unsteady flows, offering improved prediction accuracy over existing techniques like DMD and POD.

Findings

Autoencoder-LSTM achieves higher R² in flow prediction.

Autoencoder-based reduction outperforms SVD-based methods.

The combined approach effectively captures complex flow dynamics.

Abstract

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows to a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for reduced order modeling of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for long short-term memory network (LSTM) to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with non-intrusive reduced order models based on dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). Moreover, an autoencoder-DMD algorithm is introduced for reduced order modeling, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. Results show that the autoencoder-LSTM method is considerably capable of predicting fluid flow evolution, where higher values for coefficient of determination $R^{2}$ are obtained using autoencoder-LSTM compared to other models.