We enhance machine learning algorithms for learning model parameters in complex systems represented by differential equations with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, the FBPINN approach better captures the overall dynamical behavior compared to the vanilla PINN approach, even in cases with data only from a time domain with quasi-stationary dynamics.