Learning Neural Event Functions for Ordinary Differential Equations

TL;DR

This paper introduces Neural Event ODEs, extending Neural ODEs to handle implicit termination criteria and discrete events, enabling modeling of hybrid systems with instantaneous changes without prior event knowledge.

Contribution

It presents a novel framework for neural ODEs with neural event functions, allowing implicit event detection and differentiation, applicable to hybrid systems and point process modeling.

Findings

Successfully models hybrid discrete-continuous systems

Enables simulation-based training of point processes

Handles unknown number and timing of events

Abstract

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and differentiated through. Neural Event ODEs are capable of modeling discrete and instantaneous changes in a continuous-time system, without prior knowledge of when these changes should occur or how many such changes should exist. We test our approach in modeling hybrid discrete- and continuous- systems such as switching dynamical systems and collision in multi-body systems, and we propose simulation-based training of point processes with applications in discrete control.