CNN-LSTM based reduced order modeling of two-dimensional unsteady flows around a circular cylinder at different Reynolds numbers

We investigate the capability of machine learning (ML) based reduced order model (ML-ROM) for two-dimensional unsteady flows around a circular cylinder at different Reynolds numbers. The present ML-ROM is constructed by two ML schemes: a convolutional neural network-based autoencoder (CNN-AE) and a long short-term memory (LSTM). The CNN-AE is utilized to map high-dimensional flow fields obtained by direct numerical simulation (DNS) into a low-dimensional latent space while keeping their spatially coherent information. The LSTM is then trained to learn the temporal evolution of the mapped latent vectors together with the information on the Reynolds number. Using the trained LSTM model, the high-dimensional dynamics of flow fields can be reproduced with the aid of the decoder part of CNN-AE, which can map the predicted low-dimensional latent vector to the high-dimensional space. We find that the flow fields generated by the present ML-ROM show statistical agreement with the reference DNS data. The dependence of the accuracy of the proposed model on the Reynolds number is also examined in detail. The present results demonstrate that the ML-ROM can reconstruct flows at the Reynolds numbers that were not used in the training process unless the flow regime drastically changes.