# FxTS-Net: Fixed-Time Stable Learning Framework for Neural ODEs

arXiv: https://arxiv.org/abs/2411.09118 · HTML: https://mlsanity.com/paper/2411.09118/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 34 references that are in the map.
- First posted on arXiv 14 Nov 2024.

## Builds on (most cited first, 2 of 2)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)

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

- [Learning Aligned Stability in Neural ODEs Reconciling Accuracy with Robustness](https://mlsanity.com/paper/2509.21879/) (2025)
- [Stable Robot Motions on Manifolds: Learning Lyapunov-Constrained Neural Manifold ODEs](https://mlsanity.com/paper/2510.05707/) (2025)
- [Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees](https://mlsanity.com/paper/2609.32289/) (2026)

## Abstract (arXiv)

Neural Ordinary Differential Equations (Neural ODEs), as a novel category of modeling big data methods, cleverly link traditional neural networks and dynamical systems. However, it is challenging to ensure the dynamics system reaches a correctly predicted state within a user-defined fixed time. To address this problem, we propose a new method for training Neural ODEs using fixed-time stability (FxTS) Lyapunov conditions. Our framework, called FxTS-Net, is based on the novel FxTS loss (FxTS-Loss) designed on Lyapunov functions, which aims to encourage convergence to accurate predictions in a user-defined fixed time. We also provide an innovative approach for constructing Lyapunov functions to meet various tasks and network architecture requirements, achieved by leveraging supervised information during training. By developing a more precise time upper bound estimation for bounded non-vanishingly perturbed systems, we demonstrate that minimizing FxTS-Loss not only guarantees FxTS behavior of the dynamics but also input perturbation robustness. For optimising FxTS-Loss, we also propose a learning algorithm, in which the simulated perturbation sampling method can capture sample points in critical regions to approximate FxTS-Loss. Experimentally, we find that FxTS-Net provides better prediction performance and better robustness under input perturbation.