The multiscale nature and the nonlinear mechanical behavior of 3D printed lattice structures fuel the development of accurate yet efficient beam models. In particular, beam theories typically assume linear elasticity in terms of strain measures and stress resultants while hyperelasticity can only be included through the numerically expensive computation of cross-sectional deformation [1]. This raises the need for efficient data-driven surrogate models. In this contribution, we present physics-augmented neural network-based constitutive models for shear deformable Simo-Reissner beams and explore their application as surrogates in hyperelastic beam simulations. The models fulfill important mechanical conditions by construction. Strains and curvatures are used as inputs for feed-forward neural networks, which represent the hyperelastic beam potential. Forces and moments are received as the gradients of the potential ensuring thermodynamic consistency. The potential is complemented with normalization terms guaranteeing stress and energy normalization. We further extend the model to transverse isotropy and a less restrictive point symmetry to explore the implications of these constraints on the generalization and flexibility of the derived models. To improve the scaling behavior for varying cross-section radii, a data-augmentation approach is applied. Lastly, we introduce a parametrization with a scalar parameter such as the ratio between the inner and outer radius of ring-shaped cross-sections. All models are calibrated to data of circular or ring-shaped deformable hyperelastic cross-sections at varying dimensions, showing excellent accuracy and generalization. The straightforward applicability of the proposed models is further demonstrated by applying it in isogeometric beam simulations.