Comparison of reduced order models based on dynamic mode decomposition and deep learning for predicting chaotic flow in a random arrangement of cylinders

Abstract

Three reduced order models are evaluated in their capacity to predict the future state of an unsteady chaotic flow field. A spatially fully developed flow generated in a random packing of cylinders at a solid fraction of 0.1 and a nominal Reynolds number of 50 is investigated. For deep learning (DL), convolutional autoencoders are used to reduce the high-dimensional data to lower dimensional latent space representations of size 16, which were then used for training the temporal architectures. To predict the future states, two DL based methods, long short-term memory and temporal convolutional neural networks, are used and compared to the linear dynamic mode decomposition (DMD). The predictions are tested in their capability to predict the spatiotemporal variations of velocity and pressure, flow statistics such as root mean squared values, and the capability to predict fluid forces on the cylinders. Relative errors between 15% and 20% are evident in predicting instantaneous velocities, chiefly resulting from phase differences between predictions and ground truth. The spatial distribution of statistical second moments is predicted to be within a maximum of 5%–10% of the ground truth with mean error in the range of 1%–2%. Using the predicted fields, instantaneous fluid drag force predictions on individual particles exhibit a mean relative error within 20%, time-averaged drag force predictions to within 5%, and total drag force over all particles to within 1% of the ground truth values. It is found that overall, the non-linear DL models are more accurate than the linear DMD algorithm for the prediction of future states.