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

• URL: http://arxiv.org/abs/2506.06045v1
• Date: Fri, 06 Jun 2025 12:46:36 GMT
• Title: Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics
• Authors: Tobias Würth, Niklas Freymuth, Gerhard Neumann, Luise Kärger,
• Abstract summary: Rolling Diffusion-Batched Inference Network (ROBIN) is a novel learned simulator that integrates two key innovations.<n>It captures both fine-scale local dynamics and global structural effects critical for phenomena like beam bending or multi-body contact.<n>ROBIN achieves state-of-the-art accuracy on all tasks, substantially outperforming existing next-step learned simulators.
• Score: 13.41003911618347
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph-based learned simulators have emerged as a promising approach for simulating physical systems on unstructured meshes, offering speed and generalization across diverse geometries. However, they often struggle with capturing global phenomena, such as bending or long-range correlations, and suffer from error accumulation over long rollouts due to their reliance on local message passing and direct next-step prediction. We address these limitations by introducing the Rolling Diffusion-Batched Inference Network (ROBIN), a novel learned simulator that integrates two key innovations: (i) Rolling Diffusion, a parallelized inference scheme that amortizes the cost of diffusion-based refinement across physical time steps by overlapping denoising steps across a temporal window. (ii) A Hierarchical Graph Neural Network built on algebraic multigrid coarsening, enabling multiscale message passing across different mesh resolutions. This architecture, implemented via Algebraic-hierarchical Message Passing Networks, captures both fine-scale local dynamics and global structural effects critical for phenomena like beam bending or multi-body contact. We validate ROBIN on challenging 2D and 3D solid mechanics benchmarks involving geometric, material, and contact nonlinearities. ROBIN achieves state-of-the-art accuracy on all tasks, substantially outperforming existing next-step learned simulators while reducing inference time by up to an order of magnitude compared to standard diffusion simulators.

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