Turbulence Enrichment using Physics-informed Generative Adversarial Networks

TL;DR

This paper introduces physics-informed GANs for turbulence data enrichment, effectively incorporating physical constraints into generative models to produce more accurate and physically consistent turbulence simulations.

Contribution

The work develops a physics-informed loss function for GANs, improving turbulence data generation by satisfying governing equations and boundary conditions.

Findings

Physics-informed models outperform bicubic interpolation in turbulence enrichment.

Incorporating physics constraints enhances the physical accuracy of generated data.

Enriched data recovers key statistical and flow properties of turbulence.

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.