Geometric Contact Flows: Contactomorphisms for Dynamics and Control
This addresses challenges in accurately predicting dynamics for applications like fluid dynamics and robotics, though it appears incremental as it builds on existing geometric methods.
The paper tackles the problem of modeling complex dynamical systems with force exchange and dissipation by introducing Geometric Contact Flows (GCF), a framework that uses Riemannian and Contact geometry as inductive biases to learn such systems, resulting in robust generalization and adaptation to unseen scenarios in experiments on physical systems and robot control tasks.
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.