Parameter-varying neural ordinary differential equations with partition-of-unity networks
This work addresses challenges in data-driven dynamics modeling for systems with varying parameters, such as hybrid or externally forced systems, but appears incremental as it combines existing NODE and POUNet concepts.
The authors tackled the problem of modeling complex dynamical systems by proposing parameter-varying neural ordinary differential equations (NODEs) integrated with partition-of-unity networks (POUNets), which learn a meshfree partition of space and represent parameter evolution using polynomials, and demonstrated effectiveness in tasks such as hybrid systems and switching linear dynamical systems, though no concrete numerical results were provided in the 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.