(untitled) (Advances in Applied Mathematics and Mechanics, 2024)
Model Order Reduction is an approximation of the main system so that the simplified system retains important features of the main system. Deep learning technology is a recent breakthrough in artificial neural networks that can find more hidden information from the data. In this paper, a non-intrusive reduced order model (NIROM) based on combining deep neural networks (DNNs) and POD abilities, namely FAE-CAE-LSTM is presented. This method combines the obtained features based on Fully connected autoencoders (FAE), Convolutional autoencoders (CAE), and POD and then, a deep Long short-term memory network is trained by obtained features to predict the pressure and velocity fields at future time instances. We investigate the performance of the proposed methodology by solving two well-known canonical cases: a strong shear flow exhibiting the Kelvin–Helmholtz instability, and flow past a cylinder. The performance of the proposed FAE-CAE-LSTM method in future state prediction of the flow is compared with other NIROM methods such as CAE-LSTM, autoencoder-LSTM, autoencoder-DMD and POD-RNN based models. Results show that the FAE-CAE-LSTM method is considerably capable of predicting fluid flow evolution and obtains the best results in the prediction of the pressure and velocity fields in future time instances.