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

• URL: http://arxiv.org/abs/2109.01514v1
• Date: Fri, 3 Sep 2021 13:38:51 GMT
• Title: Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows
• Authors: Hamidreza Eivazi, Soledad Le Clainche, Sergio Hoyas, Ricardo Vinuesa
• Abstract summary: We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes. Our approach is based on $beta$-variational autoencoders ($beta$-VAEs) and convolutional neural networks (CNNs)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\beta$-variational autoencoders ($\beta$-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.

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