# Model Reduction of Homogeneous Polynomial Dynamical Systems via Tensor Decomposition

arXiv: https://arxiv.org/abs/2506.19165 · HTML: https://mlsanity.com/paper/2506.19165/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Structural Controllability of Large-Scale Hypergraphs](https://mlsanity.com/paper/2603.19955/) (2026)

## Abstract (arXiv)

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems that are often used to model higher-order interactions in physics, biology, and ecology, remains a significant challenge. In this article, we develop a novel model reduction method for homogeneous polynomial dynamical systems (HPDSs) with linear input and output grounded in tensor decomposition. Leveraging the inherent tensor structure of HPDSs, we construct reduced models by extracting dominant mode subspaces via higher-order singular value decomposition. Notably, we establish that key system-theoretic properties, including stability, controllability, and observability, are preserved in the reduced model. We demonstrate the effectiveness of our method using numerical examples.