Neural network based limiter with transfer learning

TL;DR

This paper introduces a neural network-based shock detection limiter that adapts across different numerical schemes and meshes, improving shock capturing in high-order methods with minimal retraining.

Contribution

It presents a transfer learning strategy for neural network shock detection, enabling adaptation to various schemes without extensive retraining or large datasets.

Findings

Neural network limiter performs comparably to traditional limiters.

Domain adaptation reduces training effort across schemes.

Computational cost remains manageable with the neural approach.

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.