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Data-driven methods have changed the way we understand and model materials.However, while providing unmatched flexibility, these methods have limitationssuch as reduced capacity to extrapolate, overfitting, and violation of physicsconstraints. Recent developments have led to modeling frameworks thatautomatically satisfy these requirements. Here we review, extend, and comparethree promising data-driven methods: Constitutive Artificial Neural Networks(CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary DifferentialEquations (NODE). Our formulation expands the strain energy potentials in termsof sums of convex non-decreasing functions of invariants and linearcombinations of these. The expansion of the energy is shared across all threemethods and guarantees the automatic satisfaction of objectivity andpolyconvexity, essential within the context of hyperelasticity. To benchmarkthe methods, we train them against rubber and skin stress-strain data. Allthree approaches capture the data almost perfectly, without overfitting, andhave some capacity to extrapolate. Interestingly, the methods find differentenergy functions even though the prediction on the stress data is nearlyidentical. The most notable differences are observed in the second derivatives,which could impact performance of numerical solvers. On the rich set of dataused in these benchmarks, the models show the anticipated trade-off betweennumber of parameters and accuracy. Overall, CANN, ICNN and NODE retain theflexibility and accuracy of other data-driven methods without compromising onthe physics. These methods are thus ideal options to model arbitraryhyperelastic material behavior.

Benchmarks for physics-informed data-driven hyperelasticity