We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment - but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity of the solution is achieved by l_p regularization combined with thresholding, which calls for a non-linear optimization scheme. The ensuing fully automated algorithm leverages physics-based constraints for the automatic determination of the penalty parameter in the regularization term. Using numerically generated data including artificial noise, we demonstrate the ability of the approach to accurately discover five hyperelastic models of different complexity. We also show that, if a "true" feature is missing in the function library, the proposed approach is able to surrogate it in such a way that the actual response is still accurately predicted.
翻译:我们提出了一种以数据驱动自动发现异位超弹性成份法的新方法。 这种方法不受监督, 也就是说, 它不需要压力数据, 只需要迁移和全球力量数据, 这些数据通过机械测试和数字图像相关技术现实可得; 它提供可解释的模型, 即通过大量候选功能目录的稀薄回归而发现的令人厌恶的数学表达方式体现的模型; 它是一粒子, 即发现只需要一个实验 - 但是如果有的话可以使用更多。 无监督的发现问题通过在大宗和已加载域边界执行均衡限制来解决。 解决方案的分化是通过 l_ p 正规化和阈值相结合实现的, 这需要非线性优化计划。 随之产生的完全自动算法将物理限制用于自动确定常规化术语中的处罚参数。 使用数字生成的数据, 包括人工噪音, 我们展示了精确发现五种不同复杂度的超弹性模型的方法的能力。 我们还表明, 如果一个“ 解释” 特性在功能库中仍然缺少一个能够预测的功能,, 我们还显示如果一个“ 精确的” 特性在这样的功能库中仍然无法预见到它的实际反应方法。