Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
This work addresses the challenge of modeling complex, high-dimensional fluid dynamics for applications in engineering and control, though it is incremental as it builds on existing deep learning techniques.
The paper tackled the problem of predicting unsteady fluid flows by introducing a deep learning-based reduced order model that combines an autoencoder for nonlinear dimension reduction with an LSTM for future state prediction, achieving higher R² values compared to traditional methods like DMD and POD.
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.