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.

翻译：近期，从数据中学习动力系统的众多成功方法相继涌现。然而，确保推断出的动力学特性能够保持已知约束（如守恒律或系统状态限制）仍具挑战。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，将其加入原始动力学方程后，可证明约束流形达到渐近稳定。得益于其简洁性，该方法兼容所有常见神经微分方程（NDE）模型，具有广泛适用性。大量实验评估表明，SNDEs在拓宽可集成到NDE训练中的约束类型的同时，性能优于现有方法。