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

TL;DR

This paper introduces a deep probabilistic neural network approach using $eta$-VAEs and CNNs to extract near-orthogonal, parsimonious non-linear modes from turbulent flow data, improving interpretability and reconstruction quality.

Contribution

The paper presents a novel $eta$-VAE-based method for non-linear mode extraction that encourages orthogonality and mode ordering, advancing flow analysis and reduced-order modeling.

Findings

Effective extraction of near-orthogonal non-linear modes from turbulent flows.

Improved flow reconstruction compared to linear and AE-based methods.

Enhanced interpretability of flow modes.

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.