对数据驱动的超弹性进行基准物理信息框架的基准测试
Vahidullah Taç1, Kevin Linka2, Francisco Sahli-Costabal3
1School of Mechanical Engineering, Purdue University, West Lafayette, USA.
Computational mechanics
|May 14, 2024
概括
三种数据驱动的方法 (构成型人工神经网络,输入形神经网络和神经普通微分方程) 准确地模拟了超弹性材料,同时尊重物理定律. 这些方法克服了传统方法的局限性,提供了更好的推断能力.
科学领域:
- 材料科学 材料科学 材料科学
- 计算力学 计算力学 计算力学
- 人工智能的人工智能
背景情况:
- 数据驱动的方法在材料建模中提供了灵活性,但存在外推问题和物理违规问题.
- 现有的方法在过度拟合和确保预测与物理约束保持一致方面扎.
研究的目的:
- 审查,扩展和比较三个以物理为基础的数据驱动的方法:构造性人工神经网络 (CANN),输入凸神经网络 (ICNN) 和神经普通微分方程 (NODE).
- 在超弹性建模中确保对客观性,材料对称性和多凸性的自动满足.
主要方法:
- 为应变能量潜力开发了一个共享的公式,将其扩展为不变数的凸非递减函数的和.
- 这三种方法 (CANN,ICNN,NODE) 使用和皮肤的应力-应变数据进行训练.
- 性能与传统的神经网络进行了基准测试,并对准确性,过拟合和推断进行了评估.
主要成果:
- 这三种基于物理的方法 (CANN,ICNN,NODE) 均准确地捕获了训练数据,并且具有最小的过拟合和证明外推能力.
- 与不受约束的网络不同,这些方法在训练范围之外产生了物理上有意义的预测.
- 虽然应力预测是相似的,但确定的能量函数有所不同,特别是在第二导数中,可能会影响数值解析器.
结论:
- CANN,ICNN和NODE成功地将数据驱动的灵活性与基于物理的约束相结合,用于超弹性材料建模.
- 这些方法为传统方法提供了强大的替代方案,克服了额外推算和物理一致性的局限性.
- 在CANN,ICNN和NODE之间做出选择可能取决于特定的应用需求和模型复杂性和准确性之间的所需权衡.
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