CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

2026-07-09 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

CaLiSym is a novel, lightweight framework that extends exact symplectic learning to complex, real-world robotic systems, including those with actuation, dissipation, and constraints. It achieves this by embedding the physical state and its interaction ports into a structured lifted canonical phase space, where the learned dynamics evolve via an exactly symplectic map. This algebraic lift avoids recurrent latent states or implicit optimization. The framework, instantiated with generalized-ridge SympNet predictors and introducing GRB-SympNet for local approximation, demonstrates significant improvements in out-of-distribution autoregressive prediction. Experiments show CaLiSym reducing OOD error by approximately 69.5% on a double pendulum (2.341 vs. 7.688) with ~3.7K parameters, achieving the lowest OOD error for a quadrotor, and reducing quadruped OOD error by 12.7% (2.697 vs. 3.089) with ~316K parameters, consistently outperforming larger baselines.

Key takeaway

For robotics engineers building dynamics models for complex, non-conservative systems, CaLiSym provides a robust solution. You can achieve significantly improved long-horizon prediction accuracy and stability, even with fewer parameters, by enforcing symplectic structure in a lifted phase space. This approach makes your models more resilient to out-of-distribution shifts and exposes energy exchange, which is crucial for advanced control synthesis. Consider integrating this structured canonical lift to enhance your robot's predictive capabilities.

Key insights

Symplectic learning extends to non-conservative systems by enforcing geometric priors in a structured, lifted phase space.

Principles

• Enforce symplecticity in a lifted canonical phase space.
• Geometric priors enhance data efficiency and stability.
• Explicit algebraic lifts enable efficient dynamics learning.

Method

Embed physical state and ports into a lifted canonical space, learn an exactly symplectic map, project back, then re-embed for autoregressive rollout.

In practice

• Model controlled dissipative systems like pendulums.
• Predict dynamics for quadrotors and quadruped robots.
• Use GRB-SympNet for low-D, GR-SympNet for high-D.

Topics

• CaLiSym
• Symplectic Learning
• Robot Dynamics
• Physics-Informed AI
• Quadruped Locomotion
• Quadrotor Control
• GRB-SympNet

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Robotics Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.