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

arXiv: https://arxiv.org/abs/2210.00368 · HTML: https://mlsanity.com/paper/2210.00368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 1 Oct 2022.

## Builds on (most cited first, 25 of 25)

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- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
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- [The gap between theory and practice in function approximation with deep neural networks](https://mlsanity.com/paper/2001.07523/) (2020)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [Recurrent switching linear dynamical systems](https://mlsanity.com/paper/1610.08466/) (2016)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Partition of unity networks: deep hp-approximation](https://mlsanity.com/paper/2101.11256/) (2021)
- [Stateful ODE-Nets using Basis Function Expansions](https://mlsanity.com/paper/2106.10820/) (2021)
- [ANODEV2: A Coupled Neural ODE Evolution Framework](https://mlsanity.com/paper/1906.04596/) (2019)
- [Growing axons: greedy learning of neural networks with application to function approximation](https://mlsanity.com/paper/1910.12686/) (2019)
- [Segmenting Hybrid Trajectories using Latent ODEs](https://mlsanity.com/paper/2105.03835/) (2021)

## Abstract (arXiv)

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.