A Self-Adaptive Penalty Method for Integrating Prior Knowledge Constraints into Neural ODEs

arXiv:2307.14940v3 Announce Type: replace
Abstract: The continuous dynamics of natural systems has been effectively modelled using Neural Ordinary Differential Equations (Neural ODEs). However, for accurate and meaningful predictions, it is crucial that the models follow the underlying rules or laws that govern these systems. In this work, we propose a self-adaptive penalty algorithm for Neural ODEs to enable modelling of constrained natural systems. The proposed self-adaptive penalty function can dynamically adjust the penalty parameters. The explicit introduction of prior knowledge …

abstract arxiv constraints continuous cs.lg differential dynamics knowledge laws math.oc natural ordinary predictions prior rules systems type work