In recent years, constitutive models based on machine learning methods have become increasingly popular, with neural networks accounting for fundamental underlying physics being the most widely used. In this contribution, we introduce a physics-augmented neural network (PANN) approach for the modeling of anisotropic finite strain elasticity [1]. It is based on the concepts of generalized structure tensors as well as isotropic tensor functions. Besides the network parameters, the structure tensors are simultaneously calibrated during training so that the underlying anisotropy of the material is reproduced most accurately. We apply the approach to several representative examples, where necessary data for the training of the PANN are collected via computational homogenization. We show that the proposed model achieves excellent interpolation and extrapolation behaviors. In the second part, we extend the PANN framework to finite strain magneto-elasticity [2]. Thus, the PANN is used to model the total energy density which describes the constitutive behavior of soft magneto-active solids. Databases for training of the models are generated via computational homogenization for quasi-incompressible magneto-active polymers. Similar to the purely elastic case, we show that the proposed model achieves excellent interpolation and extrapolation behaviors. [1] K. A. Kalina, J. Brummund, W. Sun, M. Kästner: Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions, arXiv:2410.03378, 2024. [2] K. A. Kalina, P. Gebhart, J. Brummund, L. Linden, W. Sun, M. Kästner: Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria, Computer Methods in Applied Mechanics and Engineering, 421: 116739, 2024.