Geometric Contact Flows: Contactomorphisms for Dynamics and Control

2025-06-21

AI Summary

Modeling complex dynamical systems with geometric constraints, force exchange, and energy dissipation remains challenging due to poor generalizability and limited physical consistency. Method: This paper proposes an implicit contact Hamiltonian model grounded in contact and Riemannian geometry. It introduces, for the first time, the contact diffeomorphism group as an inductive bias to construct a geometric contact flow framework that inherently enforces energy conservation, stability, and uncertainty awareness. The model integrates data-driven dynamics with physical priors via latent-space modeling and ensemble learning. Contribution/Results: Experiments demonstrate significant improvements in trajectory prediction accuracy and robustness across diverse physical systems and robot interaction control tasks. Crucially, the model exhibits strong generalization and adaptability to unseen dynamics, outperforming existing methods in both predictive fidelity and physical plausibility.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Modeling complex dynamical systems with force exchange
• Learning systems using Riemannian and Contact geometry
• Ensuring stability and energy conservation in dynamics

Innovation

• Leverages Riemannian and Contact geometry
• Constructs latent contact Hamiltonian model
• Uses ensemble of contactomorphisms for adaptation