CaLiSym: New framework brings symplectic AI to real-world robotic systems

Physics-informed machine learning promises data-efficient and stable dynamics prediction, but until now its strongest geometric guarantees applied only to closed conservative systems. This excluded most real-world robots, which constantly exchange energy and momentum through actuation, dissipation, and contact constraints. A new paper from researchers at the University of Oxford and the University of Queensland introduces CaLiSym (Canonical Lifts for Symplectic Learning), a lightweight framework that extends exact symplectic learning to these open systems by shifting where the geometric prior is imposed. Instead of forcing symplecticity on the measured physical state, CaLiSym embeds the state and its physical ports into a structured lifted canonical phase space, where the learned dynamics evolve through an exactly symplectic map. The lift is explicit and algebraic, requiring no recurrent latent states, transformer decoders, implicit optimization, or inference-time ODE integration.

The framework is instantiated with generalized-ridge SympNet predictors, and the authors introduce GRB-SympNet, a B-spline variant that combines local approximation with exact symplectic structure. Experiments on three challenging platforms — a controlled dissipative double pendulum, a real-world quadrotor, and a contact-rich quadruped — demonstrate consistent improvements in out-of-distribution autoregressive prediction while using parameter-efficient models. Notably, the learned lifted dynamics preserve the symplectic form to numerical precision. This work shows that symplectic learning can be extended beyond conservative mechanics through structured canonical lifts, paving the way for geometry-preserving dynamics models in real-world robotics and control applications.