# Geometric Contact Flows: Contactomorphisms for Dynamics and Control

arXiv: https://arxiv.org/abs/2506.17868 · HTML: https://mlsanity.com/paper/2506.17868/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [On Bringing Robots Home](https://mlsanity.com/paper/2311.16098/) (2023)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems](https://mlsanity.com/paper/2005.04986/) (2020)
- [An Extensible Benchmark Suite for Learning to Simulate Physical Systems](https://mlsanity.com/paper/2108.07799/) (2021)
- [Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)](https://mlsanity.com/paper/1806.04994/) (2018)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [Neural Canonical Transformation with Symplectic Flows](https://mlsanity.com/paper/1910.00024/) (2019)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees](https://mlsanity.com/paper/2402.08090/) (2024)
- [Learning Forceful Manipulation Skills from Multi-modal Human Demonstrations](https://mlsanity.com/paper/2109.04222/) (2021)
- [Reactive Motion Generation on Learned Riemannian Manifolds](https://mlsanity.com/paper/2203.07761/) (2022)
- [Decoder ensembling for learned latent geometries](https://mlsanity.com/paper/2408.07507/) (2024)
- [Contact Skill Imitation Learning for Robot-Independent Assembly Programming](https://mlsanity.com/paper/1908.06272/) (2019)
- [Symplectic Neural Flows for Modeling and Discovery](https://mlsanity.com/paper/2412.16787/) (2024)
- [Learning Dynamical Systems Encoding Non-Linearity within Space Curvature](https://mlsanity.com/paper/2403.11948/) (2024)
- [Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations](https://mlsanity.com/paper/2504.18860/) (2025)

## Built on by (most cited first, 2 of 2)

- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Contact Wasserstein Geodesics for Non-Conservative Schr"odinger Bridges](https://mlsanity.com/paper/2511.06856/) (2025)

## Abstract (arXiv)

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.