On the Forward Invariance of Neural ODEs
This addresses safety and reliability issues in neural ODE applications like autonomous vehicles and physical modeling, though it appears incremental as it builds on existing control barrier function methods.
The authors tackled the problem of ensuring neural ODEs satisfy output specifications by using invariance set propagation with control barrier functions, achieving guaranteed output specifications while maintaining generalization performance and enabling causal manipulation for robustness.
We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.