Towards Aerodynamic Flow Predictions with Physics-Informed Neural Networks

Abstract

Artificial neural networks have significantly transformed data-driven modeling in various fields due to their ability to describe complex and highly nonlinear relationships. Conventional neural networks typically require large amounts of training data to learn these relations. However, recent advances have adapted neural networks as an alternative approach for the approximation of solutions to partial differential equations (PDEs) without the need for solution data. Aerodynamic flows are described by the compressible Navier-Stokes equations which can be simplified to the compressible Euler equations by omitting the viscous terms. These equations model crucial sub- and supersonic flow phenomena responsible for aerodynamic responses. Classical solution methods, such as finite-volume methods, have become a valuable tool for the solution of these PDEs. However, transferring these classical approaches to potentially advantageous hardware like graphic processing units and quantum computers has shown to be challenging. Hence, our interest is to investigate alternative numerical methods based on artificial neural networks to solve the Euler and Navier-Stokes equations. Here, we investigate the physics-informed neural network (PINN) approach as an alternative method for solving the compressible Euler equations. Unlike classical neural networks, PINNs directly incorporate the PDE of interest into the loss function during the network's training process. This enables the neural network to approximate the solution to the PDE without requiring additional solution data. The presented training procedure uses artificial viscosity to stabilize the training process of PINNs. On a sub- and a supersonic test case, we illustrate that the method can obtain reasonably accurate approximations for a continuous range of inflow Mach numbers. We compare accuracy and efficiency of the method with finite volume simulations. The presented approach aims to bring the physics-informed neural network method closer to applications in aerodynamics.