Turbulence Enrichment using Physics-informed Generative Adversarial Networks

Abstract

Generative Adversarial Networks (GANs) have been widely used for generating photo-realistic images. A variant of GANs called super-resolution GAN (SRGAN) has already been used successfully for image super-resolution where low resolution images can be upsampled to a $4\times$ larger image that is perceptually more realistic. However, when such generative models are used for data describing physical processes, there are additional known constraints that models must satisfy including governing equations and boundary conditions. In general, these constraints may not be obeyed by the generated data. In this work, we develop physics-based methods for generative enrichment of turbulence. We incorporate a physics-informed learning approach by a modification to the loss function to minimize the residuals of the governing equations for the generated data. We have analyzed two trained physics-informed models: a supervised model based on convolutional neural networks (CNN) and a generative model based on SRGAN: Turbulence Enrichment GAN (TEGAN), and show that they both outperform simple bicubic interpolation in turbulence enrichment. We have also shown that using the physics-informed learning can also significantly improve the model's ability in generating data that satisfies the physical governing equations. Finally, we compare the enriched data from TEGAN to show that it is able to recover statistical metrics of the flow field including energy metrics and well as inter-scale energy dynamics and flow morphology.

arXiv commentfor associated code, see https://github.com/akshaysubr/TEGAN

References in corpus (7)

• Adam: A Method for Stochastic Optimization
• Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
• Turbulence Modeling in the Age of Data
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Super-resolution reconstruction of turbulent flows with machine learning
• Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates
• Parametrization and generation of geological models with generative adversarial networks

Cited by in corpus (12)

• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Generative Modeling of Turbulence
• Machine Learning for Physics-Informed Generation of Dispersed Multiphase Flow Using Generative Adversarial Networks
• Point-Cloud Deep Learning of Porous Media for Permeability Prediction
• Predictive data-driven model based on generative adversarial network for premixed turbulence-combustion regimes
• Generative Adversarial Networks to infer velocity components in rotating turbulent flows
• Spectrally Decomposed Diffusion Models for Generative Turbulence Recovery
• Data assimilation empowered neural network parameterizations for subgrid processes in geophysical flows
• Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer
• Rotational and Reflectional Equivariant Convolutional Neural Network for data-limited applications: Multiphase Flow demonstration
• Adversarial sampling of unknown and high-dimensional conditional distributions