Accurately predicting deformable linear object (DLO) dynamics is challenging, especially when the task requires a model that is both human-interpretable and computationally efficient. In this work, we draw inspiration from the pseudo-rigid body method (PRB) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network. This dynamics network is trained jointly with a physics-informed encoder that maps observed motion variables to the DLO's hidden state. To encourage the state to acquire a physically meaningful representation, we leverage the forward kinematics of the PRB model as a decoder. We demonstrate in robot experiments that the proposed DLO dynamics model provides physically interpretable predictions from partial observations while being on par with black-box models regarding prediction accuracy. The project code is available at: http://tinyurl.com/prb-networks