A deep-learning approach for reconstructing 3D turbulent flows from 2D observation data

Abstract

Turbulence is a complex phenomenon that has a chaotic nature with multiple spatio-temporal scales, making predictions of turbulent flows a challenging topic. Nowadays, an abundance of high-fidelity databases can be generated by experimental measurements and numerical simulations, but obtaining such accurate data in full-scale applications is currently not possible. This motivates utilising deep learning on subsets of the available data to reduce the required cost of reconstructing the full flow in such full-scale applications. Here, we develop a generative-adversarial-network (GAN)-based model to reconstruct the three-dimensional velocity fields from flow data represented by a cross-plane of unpaired two-dimensional velocity observations. The model could successfully reconstruct the flow fields with accurate flow structures, statistics and spectra. The results indicate that our model can be successfully utilised for reconstructing three-dimensional flows from two-dimensional experimental measurements. Consequently, a remarkable reduction in the complexity of the experimental setup and the storage cost can be achieved.

Physics-guided deep reinforcement learning for flow field denoising

“…In contrast to linear methods, ML-based techniques can deal with complex non-linear problems. This feature has paved the way to explore the feasibility of applying ML to various problems in complex turbulent flows [10][11][12][13][14] [15]. Several ML-based methods have been introduced considering flow reconstruction from spatially limited or corrupted data [16].…”

Multi-scale reconstruction of turbulent rotating flows with proper orthogonal decomposition and generative adversarial networks

“…In this paper, we perform a systematic quantitative comparison among three data-driven methods (no information on the underlying equations) to reconstruct highly complex two-dimensional (2-D) fields from a typical geophysical set-up, such as that of rotating turbulence. The first two methods are connected with a linear model reduction, the so-called proper orthogonal decomposition (POD) and the third is based on a fully nonlinear convolutional neural network (CNN) embedded in a framework of a generative adversarial network (GAN) (Goodfellow et al 2014;Deng et al 2019;Subramaniam et al 2020;Buzzicotti et al 2021;Guastoni et al 2021;Kim et al 2021;Buzzicotti & Bonaccorso 2022;Yousif et al 2022). Proper orthogonal decomposition is widely used for pattern recognition (Sirovich & Kirby 1987;Fukunaga 2013), optimization (Singh et al 2001) and data assimilation (Romain, Chatellier & David 2014;Suzuki 2014).…”

“…In the scenario where a large gap exists, missing both large-and small-scale features, Buzzicotti et al (2021) reconstructed for the first time a set of 2-D damaged snapshots of three-dimensional (3-D) rotating turbulence with GAN. Recent works show that CNN or GAN is also feasible to reconstruct the 3-D velocity fields with 2-D observations (Matsuo et al 2021;Yousif et al 2022). GAN consists of two CNNs, a generator and a discriminator.…”

Physics-constrained deep reinforcement learning for flow field denoising

“…2022; Yousif et al. 2023 a ), where deep learning is a subset of machine learning, in which neural networks with multiple layers are used in the model (LeCun, Bengio & Hinton 2015). The GAN-based models have shown better performance than the traditional CNN-based models.…”

“…Several supervised and unsupervised ML-based methods have been proposed for flow reconstruction from spatially limited or corrupted data (Discetti & Liu 2022). Recently, promising results have been reported from using deep learning (DL) by applying end-to-end trained convolutional neural network (CNN)-based models (Fukami, Fukagata & Taira 2019;Liu et al 2020) and generative adversarial network (GAN)-based models (Kim et al 2021;Yu et al 2022;Yousif et al 2023a), where deep learning is a subset of machine learning, in which neural networks with multiple layers are used in the model (LeCun, Bengio & Hinton 2015). The GAN-based models have shown better performance than the traditional CNN-based models.…”