ROBIN - Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics - BendingBeam Dataset

BendingBeam dataset BendingBeam is a diagnostic benchmark dataset of the paper Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics focused on structural mechanics for neural PDE solvers. It simulates the geometric nonlinear deformations of beam parts under external forces and is specifically designed to test a model's ability to propagate local boundary information across global mesh geometries. Key challenges and motivation This dataset addresses bottlenecks in learning physical dynamics on meshes. Local-to-global propagation: Force and boundary conditions are defined on a small subset of nodes (local), yet they determine the deformation of the entire part (global). Large Graph Diameters: The beams have large aspect ratios and increased mesh resolution at thin walls. This creates large graph diameters, which challenge the message-passing capabilities of graph neural networks (GNNs). Spatial Frequency Variance: Models must accurately resolve solutions across varying spatial frequencies influenced by geometry-dependent stiffness. Technical Specifications Domain: Structural Mechanics (Geometric Nonlinear Deformation)Solver: scikit-fem (Newton-Raphson, stop tolerance 10−8)Temporal Resolution: 400 time steps per simulationTotal Samples: 1,300Split: 1000 Training, 100 Validation, 100 Testing, and 100 additional. Dataset format: XDMF files based on HDF5. These simulations can be opened directly in Paraview.