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

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.

Many AI models that try to predict how 3D objects bend or change shape only focus on the surface, ignoring the object’s thickness. However, in the real world, thickness plays a major role—especially when the front and back surfaces of an object are closely related, like in plastic or metal parts. Ignoring this can lead to inaccurate predictions.We developed a new AI method that not only takes thickness into account but also follows a basic rule of geometry: if you move or rotate an object, its behavior should stay the same. This property, called equivariance, helps the AI make predictions that are more consistent and physically meaningful.Our approach runs much faster than traditional simulation tools and can still give highly accurate results. This makes it useful for industries like manufacturing, where engineers need quick and reliable ways to predict how products will perform before they are built.