Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints
This addresses the challenge of incorporating constraints into neural differential equations for researchers and practitioners in machine learning and dynamical systems, representing a novel method for a known bottleneck.
The paper tackled the problem of learning dynamical systems from data while preserving known constraints like conservation laws, proposing stabilized neural differential equations (SNDEs) that enforce arbitrary manifold constraints and outperform existing methods in evaluations.
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.