Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints

2023/06/16 by Alistair White, Niki Kilbertus, White, Alistair +5 · 5 citations
Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2306.09739

openalex publication_date 2023/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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