Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows
This work addresses the need for interpretable reduced-order modeling in fluid dynamics, specifically for turbulent flows in urban environments, but it is incremental as it builds on existing VAE and CNN methods.
The authors tackled the problem of extracting minimal and near-orthogonal non-linear modes from turbulent flow data, achieving excellent reconstruction performance compared to linear-theory-based decompositions and showing the ability to extract near-orthogonal modes for interpretability.
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control. Our approach is based on $β$-variational autoencoders ($β$-VAEs) and convolutional neural networks (CNNs), which allow us to extract non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes that may lead to interpretability.