# Tensor network subspace identification of polynomial state space models

arXiv: https://arxiv.org/abs/1709.08773 · HTML: https://mlsanity.com/paper/1709.08773/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2017.

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

- [A tensor network approach for chaotic time series prediction](https://mlsanity.com/paper/2505.17740/) (2025)

## Abstract (arXiv)

This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model is completely written in terms of a tensor network, thus avoiding the curse of dimensionality. We also prove how the block Hankel data matrices in the subspace method can be exactly represented by low rank tensor networks, reducing the computational and storage complexity significantly. The performance and accuracy of our subspace identification algorithm are illustrated by numerical experiments, showing that our tensor network implementation is around 20 times faster than the standard matrix implementation before the latter fails due to insufficient memory, is robust with respect to noise and can model real-world systems.