HyperShape: Hyperelasticity Across Diverse Shapes

Abstract

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.