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

• URL: http://arxiv.org/abs/2210.00368v1
• Date: Sat, 1 Oct 2022 20:48:01 GMT
• Title: Parameter-varying neural ordinary differential equations with partition-of-unity networks
• Abstract summary: We propose a neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets) The proposed variant of NODEs, synthesized with POUNets, learn a meshfree partition of space and represent the evolution of ODE parameters using sets of switches 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) linear dynamical systems, and (3) latent dynamics for dynamical systems with varying external forcing.
• Score: 5.885020100736158
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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