arXiv:2604.04474cs.LGcs.AI2026-04

提出可显式建模三维网格几何结构的神经网络,提升柔性体变形模拟精度。

MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation

  • 构建细胞-面-顶点间可学习映射,显式利用高维几何信息
  • 在标准数据集和金属拉伸弯曲任务中均达到当前最优性能
  • 特别适合需要精确接触与体积传播模拟的复杂变形场景

基于深度学习的方法,尤其是图神经网络(GNN),因其能处理非结构化物理场并在图结构上实现非线性回归,已在模拟固体柔性变形与接触方面崭露头角。然而,现有GNN通常仅以顶点和边构建网格图,忽视了原始几何中的高维空间特征,如二维面片和三维单元。这导致边界表示和体积特性难以准确捕捉,而这些信息对建模接触交互和内部物理量传播至关重要,尤其在稀疏网格离散下更为突出。本文提出MAVEN——一种面向三维柔性变形模拟的网格感知体积编码网络,通过显式建模更高维度的几何网格元素,实现更精确自然的物理仿真。MAVEN建立3D单元、2D面片与顶点间的可学习映射,支持灵活互转;将显式几何特征融入模型,减轻隐式学习几何模式的负担。实验结果表明,MAVEN在多个公开数据集及新型金属拉伸弯曲任务(含大变形与长期接触)中持续取得当前最优表现。

原文摘要 · Abstract (English)

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear regression on graph structures. However, existing GNNs commonly represent meshes with graphs built solely from vertices and edges. These approaches tend to overlook higher-dimensional spatial features, e.g., 2D facets and 3D cells, from the original geometry. As a result, it is challenging to accurately capture boundary representations and volumetric characteristics, though this information is critically important for modeling contact interactions and internal physical quantity propagation, particularly under sparse mesh discretization. In this paper, we introduce MAVEN, a mesh-aware volumetric encoding network for simulating 3D flexible deformation, which explicitly models geometric mesh elements of higher dimension to achieve a more accurate and natural physical simulation. MAVEN establishes learnable mappings among 3D cells, 2D facets, and vertices, enabling flexible mutual transformations. Explicit geometric features are incorporated into the model to alleviate the burden of implicitly learning geometric patterns. Experimental results show that MAVEN consistently achieves state-of-the-art performance across established datasets and a novel metal stretch-bending task featuring large deformations and prolonged contacts.

三维模拟图神经网络柔性变形几何建模

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