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：近期涌现出许多从数据中学习动力系统的成功方法。然而，确保推断出的动力学保持已知约束（如守恒定律或系统状态限制）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执行任意流形约束的方法。该方法基于稳定化项：将该项添加至原始动力学后，可证明约束流形渐近稳定。由于形式简洁，该方法兼容所有常见神经微分方程（NDE）模型并具有广泛适用性。大量实证评估表明，SNDEs在拓展可融入NDE训练的约束类型的同时，性能优于现有方法。