Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows

Abstract

Modal-decomposition techniques are computational frameworks based on data aimed at identifying a low-dimensional space for capturing dominant flow features: the so-called modes. 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 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 enable extracting 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, where the energy percentage captured by the proposed method from five modes is equal to 87.36% against 32.41% of the POD. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes with the determinant of the correlation matrix equal to 0.99, which may lead to interpretability.