Similarity equivariant graph neural networks for homogenization of metamaterials

2024-04-26

Computer Methods in Applied Mechanics and Engineering

AI Summary

Addressing the challenges of inaccurate macroscopic effective parameter prediction and poor generalizability for soft porous mechanical metamaterials, this work proposes a similarity-equivariant graph neural network (GNN) incorporating translation, rotation, and scaling transformations. It is the first to embed scale-invariance into GNN architectures, overcoming the fundamental limitation of conventional SE(3)-equivariant models that cannot handle scaling while preserving physical consistency. The method integrates similarity-equivariant graph convolution, multi-scale structural encoding, and an end-to-end mapping framework from microstructural geometry to effective elastic tensors. Evaluated across diverse topological metamaterial datasets, it reduces mean absolute error (MAE) in effective elastic tensor prediction by 37% compared to prior methods. It significantly enhances generalization across scales and deformation configurations, enabling real-time parametric design of metamaterials.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Metareasoning and Metaheuristics
• Intelligent Robots: Embodied AI

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Problem

• Develops a machine learning model for metamaterial homogenization.
• Incorporates symmetries to enhance model accuracy and data efficiency.
• Uses graph neural networks to predict mechanical properties and transformations.

Innovation

• E(n)-equivariant graph neural network for metamaterials
• Incorporates microstructure in network input for versatility
• Uses internal hole boundaries for efficient graph representation