Graph Rotation Network: Equivariant Graph Neural Network for Efficient Inverse Design in 4-D Printing

Area of Science:

• Materials Science
• Computational Science
• Machine Learning

Background:

• Designing 4-D printed structures requires achieving desired shape transformations under stimuli.
• Current machine learning (ML) methods often lack E(3) equivariance, leading to inefficient data augmentation for coordinate representation generalization.
• Existing equivariant graph neural networks (GNNs) face challenges in balancing computational efficiency and expressive power.

Purpose of the Study:

• To address the inefficiencies in ML-assisted 4-D printing design by developing an equivariant GNN.
• To introduce a novel equivariant GNN, the Graph Rotation Network (GRN), that overcomes the limitations of existing models.
• To enhance the training efficiency and predictive accuracy for 4-D printed structure design.

Main Methods:

• Proposed a novel equivariant GNN called the Graph Rotation Network (GRN).
• GRN approximates E(3) equivariant functions using a 3-D equivariant basis constructed through rotations with trainable angles.
• Theoretically analyzed E(3) equivariance and computational complexity, and empirically validated training efficiency.

Main Results:

• The GRN significantly outperformed non-equivariant GNNs and other equivariant GNNs in forward prediction tasks for 4-D printed meshes.
• Achieved 98.8% accuracy in the inverse design of 4-D printed structures.
• Demonstrated improved training efficiency due to equivariance.

Conclusions:

• The Graph Rotation Network (GRN) offers an effective and efficient solution for the design of 4-D printed structures.
• The GRN enhances the performance of ML models in predicting shape transformations and performing inverse design.
• This work provides a valuable tool for advancing 4-D printing technology through improved computational design.