mlsanityData to 7 Oct 2026

Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints

arXiv 2306.09739 ↗First posted 16 Jun 2023cs.LG physics.comp-ph stat.MLcited by 15

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Abstract (arXiv)

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations. Our approach is based on a stabilization term that, when added to the original dynamics, renders the constraint manifold provably asymptotically stable. Due to its simplicity, our method is compatible with all common neural differential equation (NDE) models and broadly applicable. In extensive empirical evaluations, we demonstrate that SNDEs outperform existing methods while broadening the types of constraints that can be incorporated into NDE training.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 40 of its 77 references that are in the map. First posted on arXiv 16 Jun 2023.

Builds on

40 of 77 references.

References · 40

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28 more
  1. 2020Normalizing Flows on Tori and Spherescited by 117
  2. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  3. 2020Neural Manifold Ordinary Differential Equationscited by 81
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Citing papers per year: 2024: 5; 2025: 5; 2026: 5.

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