When modeling viscoelasticity or kinematic hardening in plasticity, a good fit to experimental data is often obtained by introducing many instances of the same basic modeling component. In the case of the viscoelastic generalized Maxwell model, these are Maxwell chains. For kinematic hardening plasticity, a large number of back-stresses are introduced. While this approach provides a simple way to improve the models' fitting ability, it leads to many state variables. An interesting research question is therefore if fewer components, and thus also state variables, can be used while maintaining the high fitting ability. The challenge is that more complex evolution laws for the remaining state variables are required, a task perfectly suited for Physics-Enforced Neural Networks (PENNs).