用几何流建模物理系统动态，兼顾能量守恒与不确定性控制。
Geometric Contact Flows: Contactomorphisms for Dynamics and Control
- 基于黎曼与接触几何构建潜在哈密顿模型，融入稳定性约束。
- 通过接触同构族实现对真实动态的适配，保持能量守恒特性。
- 适合需高鲁棒性建模的机器人交互与复杂动力系统研究者。
准确建模和预测涉及力交换与耗散的复杂动力系统，在流体动力学、机器人等领域至关重要，但受限于几何约束与能量传递的复杂耦合。本文提出几何接触流（Geometric Contact Flows, GFC），利用黎曼几何与接触几何作为归纳偏置，学习此类系统。GFC 构建一个编码稳定性或能量守恒等性质的潜在接触哈密顿模型，并通过一组接触同构（contactomorphisms）将其适配至目标动态，同时保持这些性质。该集合允许生成具有不确定性的测地线，引导系统行为趋近数据支持区域，从而实现鲁棒泛化与未见场景适应。在物理系统动态学习及机器人交互任务控制的实验中验证了方法的有效性。
原文摘要 · Abstract (English)
Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system's behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.
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