Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
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 te...
| Authors | Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni et al. |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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