用经典实验数据对比多种机器学习材料建模方法,指导实际应用选择。
Benchmarking data-driven material models on the classic Treloar dataset

- 基于Treloar实验数据,对比五种超弹性建模框架的拟合能力。
- 所有方法均能高精度复现数据,但计算成本与参数复杂度差异显著。
- 提供选型建议,适合材料建模与机器学习交叉研究者参考。
机器学习正快速重塑本构建模,为直接从实验数据中学习材料行为提供了新途径,并挑战了长期建立的建模范式。然而,随着越来越多基于机器学习的方法涌现,它们在实际中的表现如何?本文使用经典的Treloar实验数据,对多种超弹性建模范式进行了基准测试:(广义不变量)本构人工神经网络、物理增强神经网络、(自适应)材料指纹法,以及高效无监督本构定律识别与发现方法。我们比较了它们的拟合性能、计算成本、超参数敏感性及实现难易程度。此外,讨论了预测精度与模型复杂度之间的权衡。后者通过量化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,所有方法都能出色地再现基准数据。并非单一方法胜出,而是揭示了每种方法的优势与局限,并提供了实用的使用指南。本文所有六种方法的源代码(含训练与比较脚本)、全部结果与数据均已公开,可通过 https://doi.org/10.5281/zenodo.21915635 获取。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。