Attention-based Point Cloud Networks for 3D Solid Mechanics Simulation
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This work presents a novel application of the 3DShape2VecSet architecture [1], originally developed for 3D shape representation in computer vision, to predict displacement fields from finite element method (FEM) simulations of 3D solid mechanics problems. Unlike convolutional neural network-based approaches that rely on structured grids and pose limitations in the geometric complexity of the domain, the attention-based point cloud architecture directly processes FEM mesh nodes without any interpolations. The architecture encodes FEM meshes as point clouds with associated material properties and boundary conditions, transforming them into compact latent vector representations through cross-attention. A decoder with self-attention blocks and cross-attention then predicts displacement components at mesh nodes. The architecture's flexibility extends to large deformations and hyperelastic materials exhibiting geometric and material nonlinearity. This point cloud-based approach offers a robust alternative to grid-based neural network architectures for surrogate modeling, eliminating interpolation artifacts while maintaining compatibility with standard FEM software. The predictions further act as a warm-start to the FEM solver resulting in converged solutions with significantly less iterations. [1] Zhang, B., Tang, J., Niessner, M. and Wonka, P., 3dshape2vecset: A 3d shape representation for neural fields and generative diffusion models., ACM Transactions On Graphics (TOG), 42(4), pp.1-16, 2023
