Speaker
Description
Lagrangian Neural Networks (LNNs) learn dynamical laws from trajectory data by representing a system’s Lagrangian with a neural network. In their standard formulation, however, LNNs are typically applied using carefully chosen generalized coordinates, such as angular coordinates for a pendulum, which already encode the system’s constraints and true degrees of freedom. Existing approaches permit the use of redundant Cartesian coordinates, but require the governing holonomic constraints to be supplied explicitly. We introduce, to our knowledge, the first framework that instead learns the Lagrangian and previously unknown holonomic constraints simultaneously from trajectory data. The proposed architecture consists of two jointly trained neural networks: a Lagrangian network, which learns the dynamics, and a constraint network, which discovers the constraint manifold. Derivatives obtained from the two networks are combined through the constrained Euler–Lagrange equations, coupling the learning of dynamics directly to the learning of geometry. Constraint discovery is enabled by additional loss terms enforcing geometric and kinematic consistency with the observed trajectories, and via representing the constraints as signed distance functions provides a normalized description of the same physical constraint manifold. Using pendulum systems observed only through Cartesian trajectories as representative examples, the framework recovers the hidden holonomic structure while learning dynamics that generate accurate, constraint-preserving motion. By removing the need for either predefined generalized coordinates or explicitly supplied constraint equations, this work extends LNNs to genuinely black-box settings in which only trajectory observations are available, providing a foundation for discovering both dynamical laws and unknown constraints in more complex systems, including future applications to astrophysical data.