Learning Neural Event Functions for Ordinary Differential Equations
This work addresses a specific bottleneck in continuous-time modeling for researchers in hybrid systems and control, offering an incremental extension to Neural ODEs.
The authors tackled the limitation of Neural ODEs requiring explicit termination times by introducing Neural Event ODEs, which use neural event functions to model implicit termination criteria and handle discrete changes in continuous-time systems, achieving results like modeling switching dynamics and collisions without prior knowledge of event timing or count.
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.