Thickness-aware E(3)-Equivariant 3D Mesh Neural Networks

2025-05-27

AI Summary

Existing grid-based 3D static analysis methods model only surface topology, neglecting intrinsic thickness and the physical coupling between opposing surfaces—leading to inaccurate thickness-effect modeling. This work introduces the first thickness-aware E(3)-equivariant graph neural network tailored for industrial shell structures. Our method: (1) constructs a dual-surface topological graph that explicitly encodes inter-surface correspondences and internal thickness constraints; (2) designs an E(3)-equivariant coordinate embedding mechanism to preserve geometric symmetries under rigid transformations; and (3) enables end-to-end training on real-world industrial-grade 3D shell meshes. Evaluated on a real industrial dataset, our approach significantly improves nodal displacement prediction accuracy and faithfully reproduces thickness-dependent deformation behaviors—while incurring computational overhead comparable to conventional surface-mesh-based methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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: Large pretrained models with web data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these methods primarily focus on surface topology and geometry, often overlooking the inherent thickness of real-world 3D objects, which exhibits high correlations and similar behavior between opposing surfaces. This limitation arises from the disconnected nature of these surfaces and the absence of internal edge connections within the mesh. In this work, we propose a novel framework, the Thickness-aware E(3)-Equivariant 3D Mesh Neural Network (T-EMNN), that effectively integrates the thickness of 3D objects while maintaining the computational efficiency of surface meshes. Additionally, we introduce data-driven coordinates that encode spatial information while preserving E(3)-equivariance or invariance properties, ensuring consistent and robust analysis. Evaluations on a real-world industrial dataset demonstrate the superior performance of T-EMNN in accurately predicting node-level 3D deformations, effectively capturing thickness effects while maintaining computational efficiency.

Problem

• Overcoming surface mesh limitations by integrating 3D object thickness
• Preserving computational efficiency while capturing thickness effects in deformations
• Ensuring E(3)-equivariance in data-driven 3D spatial analysis

Innovation

• Thickness-aware E(3)-Equivariant 3D Mesh Neural Network
• Data-driven coordinates preserving E(3)-equivariance
• Efficient integration of object thickness in surface meshes