# Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)

arXiv: https://arxiv.org/abs/2508.07775 · HTML: https://mlsanity.com/paper/2508.07775/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 74 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [FoundPose: Unseen Object Pose Estimation with Foundation Features](https://mlsanity.com/paper/2311.18809/) (2023)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [Deep Regression on Manifolds: A 3D Rotation Case Study](https://mlsanity.com/paper/2103.16317/) (2021)
- [HouseCat6D -- A Large-Scale Multi-Modal Category Level 6D Object Perception Dataset with Household Objects in Realistic Scenarios](https://mlsanity.com/paper/2212.10428/) (2022)
- [SecondPose: SE(3)-Consistent Dual-Stream Feature Fusion for Category-Level Pose Estimation](https://mlsanity.com/paper/2311.11125/) (2023)
- [The Double Sphere Camera Model](https://mlsanity.com/paper/1807.08957/) (2018)
- [SE3-Nets: Learning Rigid Body Motion using Deep Neural Networks](https://mlsanity.com/paper/1606.02378/) (2016)
- [Learning with 3D rotations, a hitchhiker's guide to SO(3)](https://mlsanity.com/paper/2404.11735/) (2024)
- [Tangent Space Backpropagation for 3D Transformation Groups](https://mlsanity.com/paper/2103.12032/) (2021)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Benchmarks and Challenges in Pose Estimation for Egocentric Hand Interactions with Objects](https://mlsanity.com/paper/2403.16428/) (2024)
- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [PyPose: A Library for Robot Learning with Physics-based Optimization](https://mlsanity.com/paper/2209.15428/) (2022)
- [Efficient Derivative Computation for Cumulative B-Splines on Lie Groups](https://mlsanity.com/paper/1911.08860/) (2019)
- [NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priors](https://mlsanity.com/paper/2403.03122/) (2024)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [The Oxford Multimotion Dataset: Multiple SE(3) Motions with Ground Truth](https://mlsanity.com/paper/1901.01445/) (2019)
- [Continuous-Time State Estimation Methods in Robotics: A Survey](https://mlsanity.com/paper/2411.03951/) (2024)

## Built on by (most cited first, 3 of 3)

- [Geometric Neural Distance Fields for Learning Human Motion Priors](https://mlsanity.com/paper/2509.09667/) (2025)
- [Parallelised Differentiable Straightest Geodesics for 3D Meshes](https://mlsanity.com/paper/2603.15780/) (2026)
- [PaperFit: Vision-in-the-Loop Typesetting Optimization for Scientific Documents](https://mlsanity.com/paper/2605.10341/) (2026)

## Abstract (arXiv)

Modeling the rotation of moving objects is a fundamental task in computer vision, yet SO(3) extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with SO(3) Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics