Physics-informed neural networks for solving incompressible Navier-Stokes equations in wind engineering

Abstract

Despite the substantial advancements made over the past 50 years in solving flow problems using numerical discretization of the Navier–Stokes (NS) equations, seamlessly integrating noisy data into existing algorithms remains a challenge. In addition, mesh generation is intricate, and addressing high-dimensional problems governed by parameterized NS equations is difficult. The resolution of inverse flow problems is notably resource-intensive, often necessitating complex formulations and the development of new computational codes. To address these challenges, a physics-informed neural network (PINN) has been proposed to seamlessly integrate data and mathematical models. This innovative approach has emerged as a multi-task learning framework, where a neural network is tasked with fitting observational data while reducing the residuals of partial differential equations (PDEs). This study offers a comprehensive review of the literature on the application of PINNs in solving two-dimensional and three-dimensional NS equations in structural wind engineering. While PINN has demonstrated efficacy in many applications, significant potential remains for further advancements in solving NS equations in structural wind engineering. This work discusses important areas requiring improvement, such as addressing theoretical limitations, refining implementation processes, and improving data integration strategies. These improvements are essential for the continued success and evolution of PINN in computational fluid dynamics.