AMBER: Adaptive Mesh Generation by Iterative Mesh Resolution Prediction

2025-05-29

AI Summary

To address the trade-off between mesh resolution, computational efficiency, and simulation accuracy in finite element analysis, this paper proposes an end-to-end differentiable supervised learning framework for geometry-driven adaptive mesh generation. Starting from a coarse mesh, the method iteratively predicts a local element size field and invokes a commercial mesh generator to refine the mesh. A hierarchical graph neural network models the size field, while a geometry-aware expert-label auto-projection strategy enables label-free data augmentation. The framework requires no task-specific heuristics or manual intervention and exhibits strong generalization across unseen geometries. Evaluated on 2D/3D physical problems, mechanical components, and industrial design datasets, it significantly outperforms graph networks, CNNs, and reinforcement learning baselines—achieving higher simulation accuracy without sacrificing computational efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

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.

Problem

• Adaptive mesh generation for FEM simulations
• Reducing manual design in mesh refinement
• Improving computational efficiency with AI

Innovation

• Supervised learning for adaptive mesh generation
• Hierarchical graph neural network predicts sizing field
• Data augmentation with expert label projection