Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints

arXiv:2306.09739v3 Announce Type: replace
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. …

abstract arxiv conservation constraints cs.lg data differential dynamics laws learn physics.comp-ph restrictions stat.ml systems type