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 usually occurring in solid mechanics, 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-Batched Inference (ROBI), 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.

翻译：基于图结构的学习型模拟器已成为在非结构化网格上模拟物理系统的一种有前景的方法，其在多样几何构型中展现出速度优势和泛化能力。然而，这类方法通常难以捕捉全局物理现象（如固体力学中常见的弯曲或长程关联效应），并且由于依赖局部消息传递和直接下一步预测，在长时间推演中易受误差累积的影响。为克服这些局限，我们提出了滚动扩散-批量推断网络（ROBIN），这是一种新型学习型模拟器，集成了两项关键创新：（i）滚动扩散-批量推断（ROBI），一种并行化推断方案，通过在时间窗口内重叠去噪步骤，将基于扩散的细化计算成本分摊到多个物理时间步上；（ii）基于代数多重网格粗化的分层图神经网络，支持跨不同网格分辨率的多尺度消息传递。该架构通过代数分层消息传递网络实现，能同时捕捉细尺度局部动力学和全局结构效应（对梁弯曲或多体接触等现象至关重要）。我们在涉及几何、材料和接触非线性的具有挑战性的二维与三维固体力学基准测试中验证了ROBIN。实验表明，ROBIN在所有任务上均达到最先进的精度，显著优于现有的下一步学习型模拟器，同时相比标准扩散模拟器将推断时间降低达一个数量级。