By accurately predicting industrial aging processes (IAP), such as the slow deactivation of a catalyst in a chemical plant, it is possible to schedule maintenance events further in advance, thereby ensuring a cost-efficient and reliable operation of the plant. So far, these degradation processes were usually described by mechanistic models or simple empirical prediction models. In order to accurately predict IAP, data-driven models are proposed, comparing some traditional stateless models (linear and kernel ridge regression, as well as feed-forward neural networks) to more complex stateful recurrent neural networks (echo state networks and long short-term memory networks). Additionally, variations of the stateful models are discussed. In particular, stateful models using mechanistical pre-knowledge about the degradation dynamics (hybrid models). Stateful models and their variations may be more suitable for generating near perfect predictions when they are trained on a large enough dataset, while hybrid models may be more suitable for generalizing better given smaller datasets with changing conditions.