# Geometric Contact Flows: Contactomorphisms for Dynamics and Control

**Authors:** Andrea Testa, Søren Hauberg, Tamim Asfour, Leonel Rozo  
**arXiv:** [2506.17868](https://arxiv.org/abs/2506.17868)  
**Date:** 2025-06-22  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2506.17868v1/

## Key points

- Accurate representation is essential in modeling and predicting complex dynamical systems for applications such as fluid dynamics and robotics.
- Geometric Contact Flows (GFC) framework introduced by authors Andrea Testa, Søren Hauberg, Tamim Asfour, and Leonel Rozo leverages Riemannian and Contact geometry to learn complex dynamical systems involving force exchange and dissipation.
- GFC constructs a latent contact Hamiltonian model encoding stability and energy conservation properties, utilizing an ensemble of contactomorphisms to adapt the model to target dynamics while preserving these crucial properties.
- GFC's key feature is its ability to generate uncertainty-aware geodesics guiding system behavior towards data support, enabling robust generalization and adaptation to unseen scenarios.
- Experimental results demonstrate GFC's efficacy in learning dynamics for physical systems and controlling robots in interaction tasks, showcasing its potential applicability across various domains within science and engineering.

## Summary

In the field of modeling and predicting complex dynamical systems, accurate representation is essential for various applications such as fluid dynamics and robotics. The intricate interplay of geometric constraints and energy transfer poses significant challenges in achieving this goal. To address these challenges, a novel framework called Geometric Contact Flows (GFC) has been introduced in this paper by authors Andrea Testa, Søren Hauberg, Tamim Asfour, and Leonel Rozo. GFC leverages Riemannian and Contact geometry as inductive biases to learn complex dynamical systems involving force exchange and dissipation. The framework constructs a latent contact Hamiltonian model that encodes desirable properties like stability and energy conservation. An ensemble of contactomorphisms is then utilized to adapt this model to the target dynamics while preserving these crucial properties. One key feature of GFC is its ability to generate uncertainty-aware geodesics that guide the system's behavior towards the data support. This capability enables robust generalization and adaptation to unseen scenarios, enhancing the overall effectiveness of the approach. The paper presents experimental results demonstrating the efficacy of GFC in learning dynamics for physical systems and controlling robots in interaction tasks. The findings highlight the potential of Geometric Contact Flows as a valuable tool for accurately modeling complex dynamical systems with force exchange and dissipation, showcasing its applicability across various domains within science and engineering. Accepted at ICML 2025, this research contributes significantly to advancing our understanding of dynamic systems modeling and control through innovative geometric approaches.