发表机构
Department of Engineering Science, University of Oxford; School of Mathematics and Physics, University of Sussex（牛津大学工程科学系; 萨塞克斯大学数学与物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对物理学习局限，引入CaLiSym框架，通过结构化规范提升将辛学习扩展到含能量动量交换的机器人系统。用广义岭SympNet预测器实例化，实验表明该方法能改进分布外自回归预测，保持辛形式，为现实机器人系统提供几何保持动力学模型。
AI 中文摘要
基于物理的学习有望实现数据高效且稳定的动力学预测，但其强大的几何保证大多局限于封闭保守系统，排除了许多实际的机器人系统。我们引入CaLiSym，一个轻量级框架，通过改变施加几何先验的位置，将精确辛学习扩展到此类系统。CaLiSym将状态及其物理端口嵌入结构化提升规范相空间，使学习到的动力学通过精确辛映射演化。通过广义岭SympNet预测器实例化该框架，并引入GRB - SympNet。在受控耗散双摆、实际四旋翼和富接触四足机器人上的实验表明，在使用参数高效模型时，分布外自回归预测有持续改进，且学习到的提升动力学在数值精度上保持辛形式。这些结果表明，通过结构化规范提升，辛学习可扩展到保守力学之外，为现实世界机器人系统实现几何保持动力学模型。
英文摘要
Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems. This excludes robotic systems of interest, where actuation, dissipation, and constraints exchange energy and momentum with the environment. We introduce CaLiSym, a lightweight framework that extends symplectic learning to such systems by changing where the geometric prior is imposed. Rather than enforcing symplecticity on the measured state, CaLiSym embeds the state and its ports into a lifted phase space, where the dynamics evolve through a symplectic map. The lift is explicit and algebraic, requiring neither recurrent latent states, transformer decoders, implicit optimization, nor inference-time numerical integration. We instantiate the framework with SympNet predictors and introduce GRB-SympNet, a B-spline variant combining approximation with exact symplectic structure. Experiments on a controlled dissipative double pendulum, a real-world quadrotor, and a contact-constrained real-world quadruped demonstrate the lowest out-of-distribution autoregressive rollout error across systems, improving by up to 69.5% while using fewer parameters and up to 85x fewer floating-point operations per step than sequence-model baselines. The lifted dynamics preserve the symplectic form to numerical precision, extending symplectic learning beyond conservative mechanics toward real-world robotics.
Comments19 pages, 4 figures, 5 tables
