Applications Simulation Simulation: Transactions of the Society for Modeling and Simulation International 1–19 Ó The Author(s) 2021 DOI: 10.1177/00375497211061260 journals.sagepub.com/home/sim Super-resolution of low-fidelity flow solutions via generative adversarial networks Mahdi Pourbagian 1 and Ali Ashrafizadeh 2 Abstract While computational fluid dynamics (CFD) can solve a wide variety of fluid flow problems, accurate CFD simulations require significant computational resources and time. We propose a general method for super-resolution of low-fidelity flow simulations using deep learning. The approach is based on a conditional generative adversarial network (GAN) with inexpensive, low-fidelity solutions as inputs and high-fidelity simulations as outputs. The details, including the flexible structure, unique loss functions, and handling strategies, are thoroughly discussed, and the methodology is demonstrated using numerical simulations of incompressible flows. The distinction between low- and high-fidelity solutions is made in terms of discretization and physical modeling errors. Numerical experiments demonstrate that the approach is capable of accurately forecasting high-fidelity simulations. Keywords Fluid flow simulation, low and high-fidelity CFD solution, deep learning, generative adversarial network 1. Introduction Due to the proliferation of high-performance computing resources in recent years, computational tools for simulat- ing expensive transport phenomena have become more efficient. Despite unprecedented progress, obtaining highly accurate real-time simulations remains an ambitious goal for many practical and fundamental problems, as they eas- ily exceed the capability of today’s computing resources. This can become even more challenging in demanding multiple-scale problems, such as turbulent flows, porous media, composite materials, or in iterative scenarios involving optimization, uncertainty quantification, and sensitivity analysis where hundreds of such simulations are required. As a result, a pragmatic approach would be to employ low-fidelity simulations, which introduce unde- sirable errors. The reduction of such errors has been a focus of intense research activities. Many researchers uti- lize fine-scale features to capture their effect on coarse scales, thereby increasing the accuracy of low-fidelity solutions without requiring expensive high-fidelity simula- tions. While there are numerous strategies for utilizing such correlations, deep learning tools such as neural net- works are gaining increased attention due to their recent astounding advancements. Among current deep learning techniques, generative adversarial networks (GANs) 1 have sparked great enthusiasm in the artificial intelligence community due to their versatility and interesting capabilities. Recently, a concerted effort in fluid dynamics has been launched to capitalize on the benefits of GANs. For example, in Chen et al., 2 a GAN was used to construct a low-dimensional design space of airfoil shape variations to optimize an aerodynamic design. A GAN was introduced to compress and reconstruct data in computational fluid dynamics (CFD) on computing nodes and visualization nodes. 3 Several studies have employed GANs to perform rapid graphical reconstruction and simulation of turbulent flows based on physics. 4,5 GAN was used to improve the spatial resolution of turbulent velocity fields in Deng et al. 6 In another study, CFD blood flow simulations were used to simulate in 4D flow magnetic resonance imaging (MRI) data with their associated noise distribution, and a GAN 1 Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Iran 2 The DOS (Design of Optimum Systems) Computational Research Laboratory, Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Iran Corresponding author: Mahdi Pourbagian, Faculty of Mechanical Engineering, K.N.Toosi University of Technology, No. 7, Pardis St., Molla-Sadra Avenue, Vanak Sq., 19919-43344 Tehran, Iran. Email: pourbagian@kntu.ac.ir