Abstract:We propose an interpretable deep learning (DL) model that extracts physical features from turbulence data. Based on a conditional generative adversarial network combined with a new decomposition algorithm for the Prandtl number effect, we developed a DL model that is capable of predicting the local surface heat flux very accurately using only the wall-shear stress information and Prandtl number as inputs in channel turbulence. The considered range of Prandtl number is
$Pr = 0.001 \sim 7$
… Show more
“…Specifically, U-Net architectures, which consist of a contracting path and an expansive path combined by skip connections, have demonstrated good generalization performance on unseen geometries of the fluid domain [41,42,73,74]. A popular approach to training CNNs is the generative adversarial networks (GAN) framework, which maximizes the CNNs’ ability to produce flow fields that are indistinguishable from the ground-truth fields by providing a more sophisticated loss function [63,75,76]. Figure 3Diagram of a convolution layer applied to a three-channel input of size 4×4.…”
Section: Deep-learning Fundamentalsmentioning
confidence: 99%
“…This DL framework is known as conditional generative adversarial network (cGAN) [121,122]. Despite cGANs yielding accurate data-driven solvers [75,76], the high computational cost of training the discriminator model concurrently with the solver network makes them less performant than other approaches in practice.…”
Over the last decade, deep learning (DL), a branch of machine learning, has experienced rapid progress. Powerful tools for tasks that have been traditionally complex to automate have been developed, such as image synthesis and natural language processing. In the context of simulating fluid dynamics, this has led to a series of novel DL methods for replacing or augmenting conventional numerical solvers. We broadly classify these methods into physics- and data-driven methods. Physics-driven methods, generally, tune a DL model to provide an analytical and differentiable solution to a given fluid dynamics problem by minimizing the residuals of the governing partial differential equations. Data-driven methods provide a fast and approximate solution to any fluid dynamics problem that shares some physical properties with the observations used when tuning the DL model’s parameters. Meanwhile, the symbiosis of numerical solvers and DL has led to promising results in turbulence modelling and accelerating iterative solvers. However, these methods present some challenges. Exclusively data-driven flow simulators often suffer from poor extrapolation, error accumulation in time-dependent simulations, as well as difficulties in training against turbulent flows. Substantial effort is, therefore, being invested into approaches that may improve the current state of the art.
“…Specifically, U-Net architectures, which consist of a contracting path and an expansive path combined by skip connections, have demonstrated good generalization performance on unseen geometries of the fluid domain [41,42,73,74]. A popular approach to training CNNs is the generative adversarial networks (GAN) framework, which maximizes the CNNs’ ability to produce flow fields that are indistinguishable from the ground-truth fields by providing a more sophisticated loss function [63,75,76]. Figure 3Diagram of a convolution layer applied to a three-channel input of size 4×4.…”
Section: Deep-learning Fundamentalsmentioning
confidence: 99%
“…This DL framework is known as conditional generative adversarial network (cGAN) [121,122]. Despite cGANs yielding accurate data-driven solvers [75,76], the high computational cost of training the discriminator model concurrently with the solver network makes them less performant than other approaches in practice.…”
Over the last decade, deep learning (DL), a branch of machine learning, has experienced rapid progress. Powerful tools for tasks that have been traditionally complex to automate have been developed, such as image synthesis and natural language processing. In the context of simulating fluid dynamics, this has led to a series of novel DL methods for replacing or augmenting conventional numerical solvers. We broadly classify these methods into physics- and data-driven methods. Physics-driven methods, generally, tune a DL model to provide an analytical and differentiable solution to a given fluid dynamics problem by minimizing the residuals of the governing partial differential equations. Data-driven methods provide a fast and approximate solution to any fluid dynamics problem that shares some physical properties with the observations used when tuning the DL model’s parameters. Meanwhile, the symbiosis of numerical solvers and DL has led to promising results in turbulence modelling and accelerating iterative solvers. However, these methods present some challenges. Exclusively data-driven flow simulators often suffer from poor extrapolation, error accumulation in time-dependent simulations, as well as difficulties in training against turbulent flows. Substantial effort is, therefore, being invested into approaches that may improve the current state of the art.
“…2019; Kim & Lee 2020 a ; Kim et al. 2021; Kim, Kim & Lee 2023). Lee & You (2019) also showed that GANs are better in long-term prediction of unsteady flow over a circular cylinder.…”
An accurate prediction of turbulence has been very costly since it requires an infinitesimally small time step for advancing the governing equations to resolve the fast-evolving small-scale motions. With the recent development of various machine learning (ML) algorithms, the finite-time prediction of turbulence became one of promising options to relieve the computational burden. Yet, a reliable prediction of the small-scale motions is challenging. In this study, PredictionNet, a data-driven ML framework based on generative adversarial networks (GANs), was developed for fast prediction of turbulence with high accuracy down to the smallest scale using a relatively small number of parameters. In particular, we conducted learning of two-dimensional (2-D) decaying turbulence at finite lead times using direct numerical simulation data. The developed prediction model accurately predicted turbulent fields at a finite lead time of up to half the Eulerian integral time scale over which the large-scale motions remain fairly correlated. Scale decomposition was used to interpret the predictability depending on the spatial scale, and the role of latent variables in the discriminator network was investigated. The good performance of the GAN in predicting small-scale turbulence is attributed to the scale-selection and scale-interaction capability of the latent variable. Furthermore, by utilising PredictionNet as a surrogate model, a control model named ControlNet was developed to identify disturbance fields that drive the time evolution of the flow field in the direction that optimises the specified objective function.
“…Machine-learning-based techniques in general [30][31][32] have been considered for a range of applications in fluid mechanics including turbulence modeling [33][34][35][36][37], reduced-order modeling [38][39][40][41][42], data reconstruction [43][44][45][46], and flow control [47][48][49][50][51][52]. Super-resolution reconstruction with machine learning is no exception.…”
This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction. In addition to surveying a variety of recent super-resolution applications, we provide case studies of super-resolution analysis for an example of two-dimensional decaying isotropic turbulence. We demonstrate that physics-inspired model designs enable successful reconstruction of vortical flows from spatially limited measurements. We also discuss the challenges and outlooks of machine-learning-based super-resolution analysis for fluid flow applications. The insights gained from this study can be leveraged for super-resolution analysis of numerical and experimental flow data.
Graphical abstract
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
