Parameter-varying neural ordinary differential equations with partition-of-unity networksDownload PDF

22 Sept 2022 (modified: 13 Feb 2023)ICLR 2023 Conference Withdrawn SubmissionReaders: Everyone
Keywords: neural ordinary differential equations, partition-of-unity networks, parameter-varying neural networks
TL;DR: Parameter-varying neural ODEs with spectrally represented model parameters using partition-of-unity networks
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.
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