  We introduce a data-driven framework to automatically identify interpretable
and physically meaningful hyperelastic constitutive models from sparse data.
Leveraging symbolic regression, an algorithm based on genetic programming, our
approach generates elegant hyperelastic models that achieve accurate data
fitting through parsimonious mathematic formulae, while strictly adhering to
hyperelasticity constraints such as polyconvexity. Our investigation spans
three distinct hyperelastic models -- invariant-based, principal stretch-based,
and normal strain-based -- and highlights the versatility of symbolic
regression. We validate our new approach using synthetic data from five classic
hyperelastic models and experimental data from the human brain to demonstrate
algorithmic efficacy. Our results suggest that our symbolic regression robustly
discovers accurate models with succinct mathematic expressions in
invariant-based, stretch-based, and strain-based scenarios. Strikingly, the
strain-based model exhibits superior accuracy, while both stretch- and
strain-based models effectively capture the nonlinearity and
tension-compression asymmetry inherent to human brain tissue. Polyconvexity
examinations affirm the rigor of convexity within the training regime and
demonstrate excellent extrapolation capabilities beyond this regime for all
three models. However, the stretch-based models raise concerns regarding
potential convexity loss under large deformations. Finally, robustness tests on
noise-embedded data underscore the reliability of our symbolic regression
algorithms. Our study confirms the applicability and accuracy of symbolic
regression in the automated discovery of hyperelastic models for the human
brain and gives rise to a wide variety of applications in other soft matter
systems.
