  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.
