[Paper Review] Turbulence Enrichment using Physics-informed Generative Adversarial Networks

Akshay Subramaniam, Man Long Wong+3 more|arXiv (Cornell University)|Mar 4, 2020

Advanced Image Processing Techniques27 references47 citations

TL;DR

TEGAN uses physics-informed GANs (TEResNet and TEGAN) to upsample low-resolution turbulent fields, enforcing governing equations to better recover high-frequency content and flow statistics.

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 $4 imes$ 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.

Motivation & Objective

• Motivate efficient high-fidelity turbulence data enrichment for DNS-quality statistics under computational limits.
• Develop physics-informed deep learning models that enforce Navier–Stokes constraints during upsampling.
• Compare a supervised CNN-based upsampler (TEResNet) with a SRGAN-based upsampler (TEGAN).
• Demonstrate improved physical consistency and statistical fidelity over simple interpolation.

Proposed method

• Use a GAN framework with a generator based on a deep residual network to upsample 16x16x16 low-resolution turbulence fields to 64x64x64.
• Incorporate a physics loss built from residuals of the continuity equation and the pressure Poisson equation to enforce physical realizability.
• Combine content loss (MSE and enstrophy) with physics loss to guide high-frequency content restoration.
• Train TEResNet first, then initialize and train TEGAN (generator from TEResNet, discriminator trained iteratively).
• Optionally consider future gradient-penalized WGAN and physics-based discriminator extensions.

Experimental results

Research questions

• RQ1 Can physics-informed losses improve the physical realizability of generated turbulent fields compared to unconstrained upsampling?
• RQ2 How do TEResNet and TEGAN compare in recovering high-wavenumber content and preserving turbulence statistics?
• RQ3 Do the enriched fields reproduce energy spectra, two-point correlations, and third-order statistics closer to DNS data than bicubic upsampling?
• RQ4 What is the impact of including continuity and pressure residuals on the training stability and final accuracy?

Key findings

• TEGAN and TEResNet outperform tricubic interpolation in reconstructing small-scale features.
• TEGAN reduces physics residuals by over 10% compared to TEResNet
• TEGAN and TEResNet yield similar content losses, with TE GAN achieving better physics fidelity.
• TEGAN better recovers energy spectra and two-point correlations closer to high-resolution DNS than TEResNet.
• TEGAN better represents third-order velocity correlations and Q–R diagrams, indicating improved flow morphology and energy transfer representation.