Physics-informed neural networks with coordinate transformation to solve high Reynolds number boundary layer flows

Physics-informed neural networks (PINNs) are a promising way to solve partial differential equations in forward or inverse mode. Compared with traditional numerical methods, PINNs have distinct advantages in solving inverse as well as parametric problems. However, for complicated flows such as high Reynolds number boundary layer, where large velocity gradients appear near the wall, PINNs are difficult to converge and sometimes give meaningless solutions. To deal with this issue, we introduce the coordinate transformation technique to scale up the boundary layer region and solve PINNs in a computational space where the large gradients are significantly reduced. A flat plate boundary layer and the NACA0012 airfoil are calculated, and the Reynolds number of both cases is in the order of millions. Results show that PINNs with coordinate transformation can satisfactorily solve high Reynolds boundary layer flows that are nearly impossible for vanilla PINNs.