We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of human brain tissue. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identitication and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by labelled data pairs stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion, and can thus be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise and validated on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations.

翻译：我们提出了一种自动化计算算法，用于同时实现人脑组织超弹性力学表征中的模型选择与参数识别。遵循近期提出的计算框架EUCLID（高效无监督本构定律识别与发现）的核心理念，与传统的参数标定方法不同，我们构建了一个包含文献中已知经典模型的候选超弹性模型库，并开发了一种计算策略，能够从模型库中自动选择符合实验数据且可表示为可解释符号数学表达式的模型。该计算策略包含稀疏回归（即通过稀疏性促进惩罚项正则化的回归问题，以滤除模型库中的无关模型），以及一种聚类方法，用于归并模型库中高度相关、冗余的特征。模型选择过程由不同变形模式（即单轴压缩/拉伸和简单扭转）的力学测试产生的标记数据对驱动，因此可被解释为最初提出的基于全场位移数据与全局反力信息的EUCLID方法的监督学习对应版本。该方法在含人工噪声的合成数据上进行了验证，并通过人脑标本力学测试的实验数据进行了验证，证明该方法能够发现同时具备高拟合精度与简洁可解释数学表达式的超弹性模型。