Many successful methods to learn dynamical systems from data have recently
been introduced. However, assuring 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 ordinary differential equation (NODE) models and broadly
applicable. In extensive empirical evaluations, we demonstrate that SNDEs
outperform existing methods while extending the scope of which types of
constraints can be incorporated into NODE training.

本文提出了一种基于稳定化术语的神经微分方程方法：稳定化神经微分方程，用于实现关于神经微分方程的约束条件，提出的方法简单易行，适用于常见的神经微分方程模型，并能够超越现有方法的应用范围。