发表机构
Cornell University; Neural Solid; École Polytechnique Fédérale de Lausanne (EPFL); Sandia National Laboratories（康奈尔大学; Neural Solid; 洛桑联邦理工学院; 桑迪亚国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于输入凸神经网络的凸神经势混合模型，通过PolyJet实验和Gent型基准验证其对材料组本构行为的泛化与数据效率优势。
AI 中文摘要
超弹性本构模型可用于建模弹性固体中的大变形。在常规实践中，应变能密度函数需预先指定，模型特定参数通过实验校准。然而，许多应用需要针对一组相关材料的本构模型，其力学行为随成分变化。固定的本构模型形式可能无法覆盖该组材料的全部行为范围，而拟合独立形式则无法为新成分的响应预测提供直接途径。近期研究已开发出数据驱动的本构模型，可学习灵活的应变能函数同时纳入关键物理约束。本研究中，我们提出使用基于输入凸神经网络的凸神经势混合模型，作为一种模块化且数据高效的材料组建模方法。每个势关于多凸应变不变量是凸且单调的，同时条件网络将材料描述符映射到混合权重。我们使用PolyJet 3D打印材料的实验数据和合成Gent型基准，将该方法与整体式部分输入凸神经网络进行比较。在两个基准中，混合架构对训练期间未见过的材料描述符的泛化能力更好。在PolyJet实验基准中，我们发现混合架构对模型超参数的敏感性更低；而在Gent型基准中，其在材料描述符空间的稀疏数据下泛化更可靠。这些结果表明，通过一小组共享凸神经势表示材料组，为从有限数据中学习依赖描述符的本构行为提供了有用的结构先验。
英文摘要
Hyperelastic constitutive models enable modeling large deformations in elastic solids. In common practice, a strain energy density function is prescribed in advance and model-specific parameters are calibrated from experiments. However, many applications require constitutive models for a family of related materials whose mechanical behavior varies with composition. A fixed constitutive model-form may not capture the full range of behavior across the family, while fitting separate forms does not provide a direct way to predict the response of new compositions. Recent work has developed data-driven constitutive models that learn flexible strain energy functions while incorporating key physical constraints. In this work, we propose using mixtures of convex neural potentials based on input convex neural networks as a modular and data efficient approach to modeling material families. Each potential is convex and monotonic with respect to polyconvex strain invariants, while a conditioning network maps material descriptors to mixture weights. We compare the approach with a monolithic partially input-convex neural network using experimental data from PolyJet 3D-printed materials and a synthetic Gent-type benchmark. Across both benchmarks, the mixture architecture generalized better to material descriptors not seen during training. In the PolyJet experimental benchmark, we showed that the mixture architecture is less sensitive to model hyperparameters, while in the Gent-type benchmark it generalized more reliably with sparse data in the material-descriptor space. These results suggest that representing a material family through a small set of shared convex neural potentials provides a useful structural prior for learning descriptor-dependent constitutive behavior from limited data.
Comments19 Pages, 12 Images, 4 Tables
