On the Forward Invariance of Neural ODEs

TL;DR

This paper introduces a method using invariance set propagation and control barrier functions to guarantee neural ODEs meet output specifications, enhancing robustness and safety in various applications.

Contribution

It presents a novel approach to enforce output constraints in neural ODEs through invariance set propagation and control barrier functions, applicable during training and inference.

Findings

Maintains generalization performance while enforcing constraints.

Enhances robustness and enables causal manipulation of system parameters.

Successfully applied to physical dynamics, convexity modeling, and collision avoidance.

Abstract

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.