A data-driven method has been introduced for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data.
The method utilizes the discrete Lagrange-d'Alembert principle and forced discrete Euler-Lagrange equations to construct a physically grounded model of the system's dynamics.
The dynamics are decomposed into conservative and non-conservative components, which are learned separately using feed-forward neural networks.
The approach was validated on synthetic and real-world datasets, showcasing its effectiveness in reconstructing and separating conservative and forced dynamics.