Deep learning methods for super-resolution reconstruction of turbulent flows

Abstract

Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

Unsupervised deep learning for super-resolution reconstruction of turbulence

“…2019 a , b ; Kim & Lee 2020 b ; Liu et al. 2020; Scherl et al. 2020), might be inevitable consequences of minimizing the pointwise error against the target data because the given information is insufficient to determine the solution uniquely and the target is only one of the possible solutions.…”

“…Fukami, Fukagata & Taira (2019 a , 2020 b ) and Liu et al. (2020) reconstructed a flow field from a low-resolution filtered field using a convolutional NN (CNN). The method shows significant potential.…”

Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows

“…We demonstrated that high-resolution two-dimensional turbulent flow fields of a 128 × 128 grid can be reconstructed from the input data on a coarse 4 × 4 grid via machine learning methods. Applications and extensions of SR reconstruction can be considered for not only computational (Onishi, Sugiyama & Matsuda 2019;Liu et al 2020) but also experimental fluid dynamics (Deng et al 2019;Morimoto, Fukami & Fukagata 2020). Although these attempts showed great potential of machine-learning-based SR methods to handle high-resolved fluid big data efficiently, their applicability has been so far limited only to two-dimensional spatial reconstruction.…”

“…Applications and extensions of SR reconstruction can be considered for not only computational (Onishi, Sugiyama & Matsuda 2019; Liu et al. 2020) but also experimental fluid dynamics (Deng et al. 2019; Morimoto, Fukami & Fukagata 2020).…”

Neural Networks-Based Aerodynamic Data Modeling: A Comprehensive Review

“…Fukami et al [124] adopted the CNNs and the hybrid Downsampled Skip-Connection Multi-Scale (DSC/MS) models to perform super-resolution and temporal continuity analysis to reconstruct the high-resolution turbulent flow field based on only 50 training data. Liu et al [125] proposed a novel multiple temporal paths convolutional neural network (MTPC). The MTPC model takes a time series of velocity fields as input.…”