AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction

TL;DR

AMBER is a supervised learning method that iteratively predicts mesh resolution for adaptive finite element simulations, reducing manual effort and improving accuracy across diverse geometries.

Contribution

It introduces a hierarchical graph neural network approach for automatic mesh adaptation, outperforming existing methods and generalizing to new geometries.

Findings

Outperforms recent baseline methods in accuracy.

Generalizes well to unseen geometries.

Effective on 2D and 3D datasets, including real-world designs.

Abstract

The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical regions, but typically require task-specific heuristics or cumbersome manual design by a human expert. We propose Adaptive Meshing By Expert Reconstruction (AMBER), a supervised learning approach to mesh adaptation. Starting from a coarse mesh, AMBER iteratively predicts the sizing field, i.e., a function mapping from the geometry to the local element size of the target mesh, and uses this prediction to produce a new intermediate mesh using an out-of-the-box mesh generator. This process is enabled through a hierarchical graph neural network, and relies on data augmentation by automatically projecting expert labels onto AMBER-generated data during training. We evaluate AMBER on 2D and 3D datasets, including classical physics problems, mechanical components, and real-world industrial designs with human expert meshes. AMBER generalizes to unseen geometries and consistently outperforms multiple recent baselines, including ones using Graph and Convolutional Neural Networks, and Reinforcement Learning-based approaches.