Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints

TL;DR

This paper introduces stabilized neural differential equations (SNDEs), a method that enforces arbitrary manifold constraints in neural differential equations, ensuring stability and broad applicability for learning constrained dynamical systems.

Contribution

The paper presents a simple stabilization technique for neural differential equations that guarantees asymptotic stability of constraints, compatible with existing NDE models.

Findings

SNDEs outperform existing methods in empirical evaluations.

SNDEs effectively enforce a wide range of constraints.

The method broadens the applicability of neural differential equations.

Abstract

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.