发表机构
Arizona State University（亚利桑那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
HGTO提出统一基于图的物理信息公式，将神经拓扑优化扩展到有限元图空间，耦合材料场与平衡态，以更低成本实现与常规方法相当的柔度性能。
AI 中文摘要
基于密度的拓扑优化通常被构建为材料更新、结构分析和灵敏度评估的嵌套序列。虽然神经密度参数化和双场物理信息方法提供了无数据替代方案，但大多数现有方法将密度和位移表示为坐标场，并且对有限元网格中固有的离散关系利用有限。本研究引入了HGTO，一种统一的基于图的公式，将完整的神经拓扑优化从坐标空间扩展到有限元图空间。单元密度在从网格导出的单元图上进行参数化，结构状态在相应的节点-单元超图上确定。有限元运动学、数值积分、本构响应和力组装在可微计算中保持为显式定义的操作。因此，材料场和平衡状态通过共同的有限元关联结构耦合。数值研究表明，与代表性的基于坐标的双场神经方法相比，在显著降低计算成本的情况下，柔度与常规基于密度的优化相当。相同的耦合公式适用于高分辨率和不规则网格、三维结构、有限变形和弹塑性响应。
英文摘要
Density-based topology optimization is typically structured as a nested sequence of material updates, structural analyses, and sensitivity assessments. While neural density parameterization and dual-field physics-informed approaches provide data-free alternatives, most existing methods represent density and displacement as coordinate fields and make limited use of the discrete relationships inherent in the finite element mesh. The present study introduces HGTO, a unified graph-based formulation that extends complete neural topology optimization from coordinate space to finite-element graph space. Element densities are parameterized on the element graph derived from the mesh, and the structural state is determined on the corresponding node--element hypergraph. Finite element kinematics, numerical quadrature, constitutive response, and force assembly remain explicitly defined operations within the differentiable computation. The material field and equilibrium state are therefore coupled through a common finite-element incidence structure. Numerical studies show compliance comparable to conventional density-based optimization at substantially lower computational cost than a representative coordinate-based dual-field neural method. The same coupled formulation accommodates high-resolution and irregular meshes, three-dimensional structures, finite deformation, and elastoplastic response.
