标题： 几何接触流：动力学和控制的接触同胚 显示英文标题

标题： Geometric Contact Flows: Contactomorphisms for Dynamics and Control

摘要： 准确建模和预测复杂的动力系统，特别是那些涉及力交换和耗散的系统，在从流体动力学到机器人技术的应用中至关重要，但由于几何约束和能量传递的复杂相互作用，仍然面临重大挑战。 本文介绍了几何接触流（GFC），这是一种利用黎曼几何和接触几何作为归纳偏置的新框架，用于学习此类系统。 GCF 构建了一个潜在接触哈密顿模型，编码了诸如稳定性或能量守恒等期望特性。 然后，一组接触同胚将该模型适应到目标动力学，同时保持这些特性。 这种集合允许具有不确定性的测地线，使系统的行为吸引到数据支持上，从而实现对未见过场景的鲁棒泛化和适应。 在学习物理系统的动力学以及在交互任务中控制机器人的实验中，展示了我们方法的有效性。 显示英文摘要

摘要： 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.