Potential of physics-informed neural networks for solving fluid flow problems with parametric boundary conditions

Fluid flows are present in various fields of science and engineering, so their mathematical description and modeling is of high practical importance. However, utilizing classical numerical methods to model fluid flows is often time consuming and a new simulation is needed for each modification of the domain, boundary conditions, or fluid properties. As a result, these methods have limited utility when it comes to conducting extensive parameter studies or optimizing fluid systems. By utilizing recently proposed physics-informed neural networks (PINNs), these limitations can be addressed. PINNs approximate the solution of a single or system of partial differential equations (PDEs) by artificial neural networks (ANNs). The residuals of the PDEs are used as the loss function of the ANN, while the boundary condition is imposed in a supervised manner. Hence, PDEs are solved by performing a nonconvex optimization during the training of the ANN instead of solving a system of equations. Although this relatively new method cannot yet compete with classical numerical methods in terms of accuracy for complex problems, this approach shows promising potential as it is mesh-free and suitable for parametric solution of PDE problems. This is achieved without relying on simulation data or measurement information. This study focuses on the impact of parametric boundary conditions, specifically a variable inlet velocity profile, on the flow calculations. For the first time, a physics-based penalty term to avoid the suboptimal solution along with an efficient way of imposing parametric boundary conditions within PINNs is presented.