  Forward invariance is a long-studied property in control theory that is used
to certify that a dynamical system stays within some pre-specified set of
states for all time, and also admits robustness guarantees (e.g., the
certificate holds under perturbations). We propose a general framework for
training and provably certifying robust forward invariance in Neural ODEs. We
apply this framework to provide certified safety in robust continuous control.
To our knowledge, this is the first instance of training Neural ODE policies
with such non-vacuous certified guarantees. In addition, we explore the
generality of our framework by using it to certify adversarial robustness for
image classification.
