# Learning Deep Dynamical Systems using Stable Neural ODEs

arXiv: https://arxiv.org/abs/2404.10622 · HTML: https://mlsanity.com/paper/2404.10622/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2024.

## Built on by (most cited first, 8 of 8)

- [Streaming Flow Policy: Simplifying diffusion/flow-matching policies by treating action trajectories as flow trajectories](https://mlsanity.com/paper/2505.21851/) (2025)
- [Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings](https://mlsanity.com/paper/2505.01179/) (2025)
- [Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery](https://mlsanity.com/paper/2412.07544/) (2024)
- [Tube Diffusion Policy: Reactive Visual-Tactile Policy Learning for Contact-rich Manipulation](https://mlsanity.com/paper/2604.23609/) (2026)
- [Stable Robot Motions on Manifolds: Learning Lyapunov-Constrained Neural Manifold ODEs](https://mlsanity.com/paper/2510.05707/) (2025)
- [A Robust Task-Level Control Architecture for Learned Dynamical Systems](https://mlsanity.com/paper/2511.09790/) (2025)
- [Generative prediction of laser-induced rocket ignition with dynamic latent space representations](https://mlsanity.com/paper/2603.07525/) (2026)
- [Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees](https://mlsanity.com/paper/2609.32289/) (2026)

## Abstract (arXiv)

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories; however, they have three shortcomings: a) the DS is assumed to have a single attractor, which limits the diversity of tasks it can achieve, b) state derivative information is assumed to be available in the learning process and c) the state of the DS is assumed to be measurable at inference time. We propose a class of provably stable latent DS with possibly multiple attractors, that inherit the training methods of Neural Ordinary Differential Equations, thus, dropping the dependency on state derivative information. A diffeomorphic mapping for the output and a loss that captures time-invariant trajectory similarity are proposed. We validate the efficacy of our approach through experiments conducted on a public dataset of handwritten shapes and within a simulated object manipulation task.