Finite element inspired networks: Learning physically-plausible deformable object dynamics from partial observations

The accurate simulation of deformable linear object (DLO) dynamics is challenging if the task at hand requires a human-interpretable and data-efficient model that also yields fast predictions. To arrive at such model, we draw inspiration from the rigid finite element method (R-FEM) and model a DLO as a serial chain of rigid bodies whose internal state is unrolled through time by a dynamics network. As this state is not observed directly, the dynamics network is trained jointly with a physics-informed encoder mapping observed motion variables to the body chain's state. To encourage that the state acquires a physically meaningful representation, we leverage the forward kinematics (FK) of the underlying R-FEM model as a decoder. We demonstrate in a robot experiment that this architecture - being termed "Finite element inspired network" - forms an easy to handle, yet capable DLO dynamics model yielding physically interpretable predictions from partial observations. The project code is available at: \url{https://tinyurl.com/fei-networks}