Herein, a neural network-based constitutive model for isotropic hyperelastic solids which makes use of a physically motivated dimensionality reduction into the invariant space is presented. In order to automatically fulfill thermodynamic consistency, gradients of the network with respect to the input quantities are considered within a customized training loop. The proposed approach is exemplarily applied to the finite element simulation of two three-dimensional samples, while only data collected from pure two-dimensional virtual experiments are needed for the model calibration before.