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Many successful methods to learn dynamical systems from data have recentlybeen introduced. However, ensuring that the inferred dynamics preserve knownconstraints, such as conservation laws or restrictions on the allowed systemstates, remains challenging. We propose stabilized neural differentialequations (SNDEs), a method to enforce arbitrary manifold constraints forneural differential equations. Our approach is based on a stabilization termthat, when added to the original dynamics, renders the constraint manifoldprovably asymptotically stable. Due to its simplicity, our method is compatiblewith all common neural differential equation (NDE) models and broadlyapplicable. In extensive empirical evaluations, we demonstrate that SNDEsoutperform existing methods while broadening the types of constraints that canbe incorporated into NDE training.

Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints