The multiscale nature and the nonlinear mechanical behavior of 3D printed lattice structures fuel the development of more accurate yet efficient beam models. In particular, beam theories typically assume linear elasticity in terms of strain measures and effective stress measures while nonlinear, hyperelastic material behavior can only be included through the numerically expensive computation of cross-sectional deformation [1]. In this contribution, a neural network (NN) based model for hyperelastic beams subjected to large strain and large deformation is presented. It exploits the nonlinear, high-dimensional interpolation capabilities of NNs and captures the material response directly through stress and strain measures without the need for numerical integration over the cross-section. The model fulfills thermodynamic consistency as well as stress and energy normalization by construction and can be extended with point symmetry for beams where the material distribution in the cross-section is point symmetric to the center of mass. To account for different radii, a physically motivated parameterization is introduced. Calibration and test data was generated with a finite element implementation of the geometrically exact beam model, which solves the cross-sectional warping problem [1]. The strain measures were sampled using a concentric sampling strategy, which ensures physical admissibility and sensibility of every data point. The NN model achieves excellent accuracy on univariate and mixed load paths with strain amplitudes up to 0.5 and good accuracy for even larger strains. The radius-parameterized model enables good approximations for circular beams with radius to length ratios greater 0.04.