  Data-driven methods have changed the way we understand and model materials.
However, while providing unmatched flexibility, these methods have limitations
such as reduced capacity to extrapolate, overfitting, and violation of physics
constraints. Recent developments have led to modeling frameworks that
automatically satisfy these requirements. Here we review, extend, and compare
three promising data-driven methods: Constitutive Artificial Neural Networks
(CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential
Equations (NODE). Our formulation expands the strain energy potentials in terms
of sums of convex non-decreasing functions of invariants and linear
combinations of these. The expansion of the energy is shared across all three
methods and guarantees the automatic satisfaction of objectivity and
polyconvexity, essential within the context of hyperelasticity. To benchmark
the methods, we train them against rubber and skin stress-strain data. All
three approaches capture the data almost perfectly, without overfitting, and
have some capacity to extrapolate. Interestingly, the methods find different
energy functions even though the prediction on the stress data is nearly
identical. The most notable differences are observed in the second derivatives,
which could impact performance of numerical solvers. On the rich set of data
used in these benchmarks, the models show the anticipated trade-off between
number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the
flexibility and accuracy of other data-driven methods without compromising on
the physics. These methods are thus ideal options to model arbitrary
hyperelastic material behavior.
