用自适应网格分块提升可变形体模拟效率,支持超大规模网格。
Learning Deformable Body Interactions With Adaptive Spatial Tokenization
- 将不规则网格映射到规则网格,动态生成稀疏令牌表示物理状态。
- 在超过10万节点的大型模拟中仍保持高效,准确率显著优于现有方法。
- 适合需要高精度、大尺度可变形体模拟的研究者使用。
模拟可变形体之间的相互作用在材料科学、机械设计和机器人领域至关重要。基于学习的方法(如图神经网络)虽能有效处理复杂物理系统,但在建模可变形体交互时面临可扩展性问题:需动态创建成对全局边,计算开销巨大,难以应对大规模网格。为此,受几何表示启发,本文提出自适应空间令牌化(AST)方法,实现物理状态的高效表示。通过将仿真空间划分为网格单元,并将无结构网格映射至该结构化网格,自然聚合相邻网格节点。随后利用交叉注意力模块将稀疏单元压缩为固定长度嵌入,作为整个物理状态的令牌。再通过自注意力模块在潜在空间中预测下一时刻状态。该框架结合了令牌化的效率与注意力机制的表达能力,实现了高精度且可扩展的模拟结果。大量实验表明,本方法在可变形体交互建模上显著超越当前最优方案。尤其在超过10万节点的大规模模拟中仍表现良好,而现有方法因计算限制无法适用。此外,我们还构建了一个包含多种可变形体交互的新型大规模数据集,以支持未来研究。
原文摘要 · Abstract (English)
Simulating interactions between deformable bodies is vital in fields like material science, mechanical design, and robotics. While learning-based methods with Graph Neural Networks (GNNs) are effective at solving complex physical systems, they encounter scalability issues when modeling deformable body interactions. To model interactions between objects, pairwise global edges have to be created dynamically, which is computationally intensive and impractical for large-scale meshes. To overcome these challenges, drawing on insights from geometric representations, we propose an Adaptive Spatial Tokenization (AST) method for efficient representation of physical states. By dividing the simulation space into a grid of cells and mapping unstructured meshes onto this structured grid, our approach naturally groups adjacent mesh nodes. We then apply a cross-attention module to map the sparse cells into a compact, fixed-length embedding, serving as tokens for the entire physical state. Self-attention modules are employed to predict the next state over these tokens in latent space. This framework leverages the efficiency of tokenization and the expressive power of attention mechanisms to achieve accurate and scalable simulation results. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art approaches in modeling deformable body interactions. Notably, it remains effective on large-scale simulations with meshes exceeding 100,000 nodes, where existing methods are hindered by computational limitations. Additionally, we contribute a novel large-scale dataset encompassing a wide range of deformable body interactions to support future research in this area.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。