In recent years, constitutive models based on machine learning methods have become increasingly popular, with neural networks (NNs) being the most popular approach. There is general consensus that NN-based constitutive models should integrate physical knowledge. This talk gives an overview on the concept of physics-augmented neural networks (PANNs) [1] for the modeling of viscoelasticity. Thereby, it is the core idea of PANNs to enforce physical conditions by construction. We begin with a PANN model for compressible small strain viscoelasticity [2]. This approach relies on the theory of generalized standard materials (GSMs), which introduces two scalar-valued potentials such that the constitutive model is thermodynamically consistent by construction. In addition, further physical principles are also encoded in the network architecture through invariant-based formulations of the respective potentials. We show how the model can be trained using stress-strain tuples and supervised learning. To this end, a constrained optimization problem, which is subject to the algorithmic solution of the evolutionary equations, has to be solved. Afterwards, it is discussed how the viscoelastic PANN can be calibrated using full-field data and unsupervised learning strategies. In the second part of the talk, we extend the PANN approach towards incompressible finite strain viscoelasticity [3]. To demonstrate the model’s performance, we calibrate it via experimental data from literature and compare it with a classical model. REFERENCES [1] L. Linden, D. K. Klein, K. A. Kalina, J. Brummund, O. Weeger and M. Kästner. Neural networks meet hyperelasticity: A guide to enforcing physics. Journal of the Mechanics and Physics of Solids, Vol. 179, p. 105363, 2023. [2] M. Rosenkranz, K. A. Kalina, J. Brummund, W. Sun and M. Kästner. Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables. Computational Mechanics, Vol. 74, pp. 1279-1301, 2024. [3] K. A. Kalina, J. Brummund, M. Kästner. A physics-augmented neural network framework for finite strain incompressible viscoelasticity. Preprint, 2025, arXiv:2511.02959.