发表机构
Friedrich-Alexander-Universität Erlangen-Nürnberg; Stanford University（弗里德里希-亚历山大-埃尔兰根-纽伦堡大学; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究以Treloar数据集为基准，对比多种超弹性机器学习框架的性能、成本等，明确各方法优缺并提供应用指导，相关代码与数据公开。
AI 中文摘要
机器学习正迅速重塑本构建模领域，为直接从实验数据中学习材料行为提供了新方法，也对长期确立的建模范式提出了挑战。但随着越来越多基于机器学习的方法出现，它们在实际应用中如何对比？本文采用经典的Treloar实验数据，对流行的超弹性框架进行基准测试，这些框架包括（广义不变量）本构人工神经网络、物理增强神经网络、（自适应）材料指纹，以及高效无监督本构定律识别与发现。我们对比了它们的拟合性能、计算成本、超参数敏感性和实现便捷性。此外，我们还讨论了预测精度与模型复杂度之间的权衡，其中模型复杂度通过量化所发现模型中的材料参数数量，以及评估本构模型及其导数所需的计算时间来衡量。结果表明，所有方法都能极好地重现基准数据。我们并未确定单一最优方法，而是强调了每种方法的优势与局限性，并为其应用提供实用指导。本研究中所有六种方法的源代码，包括训练脚本和对比脚本，以及所有结果和所用数据，都可通过该httpsURL公开获取。
英文摘要
Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms. But with a growing number of machine-learning-based approaches available, how do they compare in practice? In this paper, we use the classic experimental data of Treloar to benchmark popular frameworks for hyperelasticity: (Generalized-Invariant) Constitutive Artificial Neural Networks, Physics-Augmented Neural Networks, (Adaptive) Material Fingerprinting, and Efficient Unsupervised Constitutive Law Identification & Discovery. We compare their fitting performance, computational cost, hyperparameter sensitivity, and ease of implementation. Furthermore, we discuss the trade-offs between predictive accuracy and model complexity. The latter is assessed by quantifying both the number of material parameters in the discovered models and the computational time required to evaluate the constitutive model and its derivatives. The results show that all methods can reproduce the benchmark data remarkably well. Rather than identifying a single winner, we highlight the strengths and limitations of each approach and provide practical guidance for their use. The source code for all six methods, including the training and comparison scripts, as well as all results and data used in this study, is publicly available via https://doi.org/10.5281/zenodo.21915635.
Comments27 pages, 8 figures, 7 tables
