Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations

TL;DR

This paper introduces AMBER, an imitation learning approach using graph neural networks to iteratively predict expert-like adaptive meshes, improving simulation accuracy and efficiency in complex physical systems.

Contribution

AMBER is a novel method that models adaptive mesh generation as an imitation learning problem, combining GNNs with online data acquisition for iterative mesh refinement.

Findings

AMBER closely matches expert mesh resolutions in 2D and 3D.

It outperforms single-step CNN baselines in accuracy.

The iterative approach improves simulation efficiency.

Abstract

Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost and accuracy of the FEM scale with the resolution of the underlying computational mesh. To balance computational speed and accuracy meshes with adaptive resolution are used, allocating more resources to critical parts of the geometry. Currently, practitioners often resort to hand-crafted meshes, which require extensive expert knowledge and are thus costly to obtain. Our approach, Adaptive Meshing By Expert Reconstruction (AMBER), views mesh generation as an imitation learning problem. AMBER combines a graph neural network with an online data acquisition scheme to predict the projected sizing field of an expert mesh on a given intermediate mesh, creating a more accurate subsequent mesh. This iterative process ensures efficient and accurate imitation of expert mesh resolutions on arbitrary new geometries during inference. We experimentally validate AMBER on heuristic 2D meshes and 3D meshes provided by a human expert, closely matching the provided demonstrations and outperforming a single-step CNN baseline.