Neural network based limiter with transfer learning

Abstract: A neural network is trained using simulation data from a Runge Kutta discontinuous Galerkin (RKDG) method and a modal high order limiter. With this methodology, we design one and two-dimensional black-box shock detection functions. Furthermore, we describe a strategy to adapt the shock detection function to different numerical schemes without the need of a full training cycle and large dataset. We evaluate the performance of the neural network on a RKDG scheme for validation. To evaluate the domain adaptation properties of this neural network limiter, our methodology is verified on a residual distribution scheme (RDS), both in one and two-dimensional problems, and on Cartesian and unstructured meshes. Lastly, we report on the quality of the numerical solutions when using a neural based shock detection method, in comparison to more traditional limiters, as well as on the computational impact of using this method in existing codes.