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.

翻译：近年来，许多成功从数据中学习动力系统的方法被引入。然而，确保推断出的动力学能保持已知约束（如守恒定律或对系统允许状态的限制）仍具挑战性。我们提出稳定化神经微分方程（SNDEs），一种为神经微分方程强制施加任意流形约束的方法。该方法基于一个稳定化项，该项加入原始动力学后，能使约束流形可证明地渐近稳定。由于其简洁性，我们的方法兼容所有常见神经常微分方程（NODE）模型，并具有广泛适用性。大量实证评估表明，SNDEs在扩展可纳入NODE训练的约束类型范围的同时，性能优于现有方法。