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

TL;DR

This paper introduces T-EMNN, a novel 3D mesh neural network that incorporates object thickness and E(3)-equivariance, improving deformation predictions while maintaining efficiency.

Contribution

The work presents a new framework that integrates thickness information into E(3)-equivariant mesh neural networks, addressing a key limitation of surface-only analysis methods.

Findings

T-EMNN outperforms existing models in deformation prediction accuracy.

The method effectively captures thickness effects in 3D objects.

It maintains computational efficiency comparable to surface mesh methods.

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.