AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction
This addresses the need for efficient and automated mesh adaptation in computational physics, reducing reliance on manual design, but it is incremental as it builds on existing learning methods.
The paper tackles the problem of adaptive mesh generation for finite element simulations by proposing AMBER, a supervised learning approach that iteratively predicts sizing fields to refine meshes, achieving consistent outperformance over multiple recent baselines on 2D and 3D datasets.
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.