Deep Convolutional Generative Adversarial Networks Applied to 2D Incompressible and Unsteady Fluid Flows

Abstract

In this work, we are studying the use of Deep Convolutional Generative Adversarial Networks (DCGANs) for numerical simulations in the field of Computational Fluid Dynamics (CFD) for engineering problems. We claim that these DCGANs could be used in order to represent in an efficient fashion high-dimensional realistic samples. Let us take the example of fluid flows’ unsteady velocity and pressure fields computation when subjected to random variations associated for example with different design configurations or with different physical parameters such as the Reynolds number and the boundary conditions. The evolution of all these variables is usually very hard to parameterize and to reproduce in a reduced order space. We would like to be able to reproduce the time coherence of these unsteady fields and their variations with respect to design variables or physical ones. We claim that the use of the data generation field in Deep Learning will enable this exploration in numerical simulations of large dimensions for CFD problems in engineering sciences. Therefore, it is important to precise that the training procedure in DCGANs is completely legitimate because we need to explore afterwards large dimensional variabilities within the Partial Differential Equations. In literature it is stated that theoretically the generative model could learn to memorize training examples, but in practice it is shown that the generator did not memorize the training samples and was capable of generating new realistic ones. In this work, we show an application of DCGANs to a 2D incompressible and unsteady fluid flow in a channel with a moving obstacle inside. The input of the DCGAN is a Gaussian vector field of dimension 100 and the outputs are the generated unsteady velocity and pressure fields in the 2D channel with respect to time and to an obstacle position. The training set is constituted of 44 unsteady and incompressible simulations of 450 time steps each, on a cartesian mesh of dimension $79\times 99$. We discuss the architectural and the optimization hyper-parameters choice in our case, following guidelines from the literature on stable GANs. We quantify the GPU cost needed to train a generative model to the 2D unsteady flow fields, to 892 s on one Nvidia Tesla V100 GPU, for 40 epochs and a batch size equal to 128.