# Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling

arXiv: https://arxiv.org/abs/2001.02861 · HTML: https://mlsanity.com/paper/2001.02861/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [State-Space Kolmogorov Arnold Networks for Interpretable Nonlinear System Identification](https://mlsanity.com/paper/2506.16392/) (2025)
- [Decoupling multivariate functions using a nonparametric filtered tensor decomposition](https://mlsanity.com/paper/2205.11153/) (2022)
- [Autoregressive models for biomedical signal processing](https://mlsanity.com/paper/2304.11070/) (2023)
- [Making Tensor Decoupling More Robust and Less Parametric](https://mlsanity.com/paper/2610.16937/) (2026)

## Abstract (arXiv)

Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over complexity, making too complex models unfit or undesired. In this work, the complexity of such models is reduced by retrieving a more structured, parsimonious model from the data, without exploiting physical knowledge. Essential to the method is a translation of all multivariate nonlinear functions, typically found in nonlinear state-space models, into sets of univariate nonlinear functions. The latter is computed from a tensor decomposition. It is shown that typically an excess of degrees of freedom are used in the description of the nonlinear system whereas reduced representations can be found. The method yields highly structured state-space models where the nonlinearity is contained in as little as a single univariate function, with limited loss of performance. Results are illustrated on simulations and experiments for: the forced Duffing oscillator, the forced Van der Pol oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.