Maintenance of engineering assets (for example, aircraft, jet engines, and wind turbines) is a profitable business. Unfortunately, building models that estimate remaining useful life for large fleets is daunting due to factors such as duty cycle variation, harsh environments, inadequate maintenance, and mass production problems that cause discrepancies between designed and observed lives. We model cumulative damage through recurrent neural networks. Besides architectures such as long short-term memory and gated recurrent unit, we introduced a novel physics-informed approach. Essentially, we merge physics-informed and data-driven layers. With that, engineers and scientists can use physics-informed layers to model well understood phenomena (for example, fatigue crack growth) and use data-driven layers to model poorly characterized parts (for example, internal loads). A numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network. The problem consists of predicting fatigue crack length for a fleet of aircraft. The models are trained using full input observations (far-field loads) and very limited output observations (crack length data for only a portion of the fleet). The results demonstrate that our proposed physics-informed recurrent neural network can model fatigue crack growth even when the observed distribution of crack length does not match the fleet distribution.