HyperShape：跨多种形状的超弹性研究
HyperShape: Hyperelasticity Across Diverse Shapes
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中文总结 AI 辅助
HyperShape是可生成多复杂度2D/3D超弹性数据集的框架，用于评估神经算子的跨形状泛化能力，发现现有神经算子在复杂形状上性能不足，需进一步开发。
中文摘要 AI 辅助
超弹性变形对域几何和边界条件高度敏感，因此跨这些因素的泛化能力是应用于超弹性问题的神经算子的关键能力。然而，现有的超弹性神经算子基准依赖于简单或少量几何结构，难以严格评估该能力。为解决这一缺口，我们推出HyperShape，这是一个可扩展的框架，旨在生成合成形状及其对应的超弹性模拟数据，产出一套具有可调节复杂度和可控形状变化的2D及3D数据集。该设计支持对分布内、分布外及合成到真实迁移场景下的泛化能力进行系统评估。我们使用该框架评估了多种最先进神经算子在不同形状分布上的性能。研究发现，神经算子在简单形状上表现良好，但随着形状复杂度、几何多样性和边界条件可变性的提升，其表现会下降，且在这类场景中需要大量训练数据。性能随几何复杂度的提升持续且可预测地下降，凸显了进一步开发模型的必要性。作为一个开放且可扩展的基准，HyperShape旨在随领域发展而成长：新的几何结构、材料模型、载荷条件和评估设置均可轻松纳入，以验证超弹性替代模型。
英文摘要
Hyperelastic deformations are highly sensitive to domain geometry and boundary conditions, making generalization across both a critical capability for neural operators applied to these problems. However, existing benchmarks for neural operators on hyperelasticity rely on simple or few geometries, which makes it difficult to assess this capability rigorously. To address this gap, we introduce HyperShape, an extensible framework designed to generate synthetic shapes and their corresponding hyperelastic simulation data, producing a suite of 2D and 3D datasets with adjustable complexity and controllable shape variations. This design enables systematic assessment of generalization across in-distribution, out-of-distribution, and synthetic-to-real transfer settings. Using this framework, we evaluated the performance of several state-of-the-art neural operators over diverse shape distributions. Our findings reveal that neural operators perform well on simple shapes but struggle as shape complexity, geometric diversity, and boundary condition variability increase, requiring large amounts of training data in such regimes. Performance degrades consistently and predictably with geometric complexity highlighting the need for further model development. As an open and extensible benchmark, HyperShape is designed to grow alongside the field: new geometries, material models, loading conditions, and evaluation settings can be easily incorporated to validate hyperelastic surrogate models.
发表机构
- University of Basel（巴塞尔大学）
- Inria（法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。
