Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
Abstract
We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.
Cite
@article{arxiv.2605.10613,
title = {Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality},
author = {Feliciano Giuseppe Pacifico and Duccio Fanelli and Lorenzo Buffoni and Lorenzo Chicchi and Diego Febbe and Raffaele Marino},
journal= {arXiv preprint arXiv:2605.10613},
year = {2026}
}
Comments
15 pages, 3 figures