The manipulation of deformable linear objects (DLOs) via model-based control requires an accurate and computationally efficient dynamics model. Yet, data-driven DLO dynamics models require large training data sets while their predictions often do not generalize, whereas physics-based models rely on good approximations of physical phenomena and often lack accuracy. To address these challenges, we propose a physics-informed neural ODE capable of predicting agile movements with significantly less data and hyper-parameter tuning. In particular, we model DLOs as serial chains of rigid bodies interconnected by passive elastic joints in which interaction forces are predicted by neural networks. The proposed model accurately predicts the motion of an robotically-actuated aluminium rod and an elastic foam cylinder after being trained on only thirty seconds of data. The project code and data are available at: \url{https://tinyurl.com/neuralprba}
