Learning Neural Event Functions for Ordinary Differential Equations

Ricky T. Q. Chen, Brandon Amos, Maximilian Nickel

Keywords: differential equations, implicit differentiation, point processes

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.

One-sentence Summary: We discuss how event handling in ODE solvers can be differentiated through, allowing us to extend Neural ODEs to cases of implicitly defined termination times and enabling learning of discrete events and discontinuous dynamics.

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Code: [ rtqichen/torchdiffeq](https://github.com/rtqichen/torchdiffeq)

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2011.03902/code)