FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs

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 in two settings: certified safety in robust continuous control, and certified adversarial robustness for image classification. To our knowledge, this is the first instance of training NODE policies with such non-vacuous certified guarantees.