  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.
