This paper presents a novel data-driven framework for simultaneously discovering appropriate invariants and constitutive models for isotropic incompressible hyperelastic materials. It uses an approach that directly identifies the most appropriate invariants and corresponding strain energy functions from a generalized class of invariants from experimental observations. Unlike existing methods that rely on fixed invariant selection or sequential fitting procedures, our method integrates the discovery process into a single neural network architecture. By considering a continuous set of invariants, it can flexibly adapt to diverse material behaviors. We demonstrate the effectiveness of this method using existing benchmark datasets for rubber and brain tissue. For rubber, we recover a stretch-dominant formulation consistent with existing models, while for brain tissue, we identify a formulation sensitive to small stretches, capturing the nonlinear shear response characteristics of soft biological materials. Compared to existing and neural network-based models, we improve predictive accuracy and interpretability across a wide range of strains. This integrated strategy provides a powerful tool for automated and physically meaningful model discovery in hyperelastic materials.
