Modeling of Inviscid Flow Shock Formation in a Wedge-Shaped Domain Using a Physics-Informed Neural Network-Based Partial Differential Equation Solver

Physics-informed neural networks (PINN) can potentially be applied to develop computationally efficient surrogate models, perform anomaly detection, and develop time-series forecasting models. However, predicting small-scale features such as the exact location of shocks and the associated rapid changes in fluid properties across it, have proven to be challenging when using standard PINN architectures, due to spatial biasing during network training. This paper investigates the ability of PINNs to capture these features of an oblique shock by applying Fourier feature network architectures. Four PINN architectures are applied namely a standard PINN architecture with the direct and indirect implementation of the ideal gas equation of state, as well as the direct implementation combined with a standard and modified Fourier feature transformation function. The case study is 2D steady-state compressible Euler flow over a 15° wedge at a Mach number of 5. The PINN predictions are compared to results generated using proven numerical CFD techniques. The results show that the indirect implementation of the equation of state is unable to enforce the prescribed boundary conditions. The application of the Fourier feature up-sampling to the low-dimensional spatial coordinates improves the ability of the PINN model to capture the small-scale features, with the standard implementation performing better than the modified version.