Parameter-varying neural ordinary differential equations with partition-of-unity networks

TL;DR

This paper introduces parameter-varying neural ODEs using partition-of-unity networks, enabling flexible modeling of systems with changing dynamics across different regions.

Contribution

It presents a novel NODE variant with POUNets that learn meshfree partitions and polynomial parameter evolution, applicable to hybrid, switching, and externally forced systems.

Findings

Effective modeling of hybrid systems.

Successful application to switching linear systems.

Accurate latent dynamics with varying external forcing.

Abstract

In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed variant of NODEs, synthesized with POUNets, learn a meshfree partition of space and represent the evolution of ODE parameters using sets of polynomials associated to each partition. We demonstrate the effectiveness of the proposed method for three important tasks: data-driven dynamics modeling of (1) hybrid systems, (2) switching linear dynamical systems, and (3) latent dynamics for dynamical systems with varying external forcing.