# Initialization Approach for Nonlinear State-Space Identification via the Subspace Encoder Approach

arXiv: https://arxiv.org/abs/2304.02119 · HTML: https://mlsanity.com/paper/2304.02119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [On the smoothness of nonlinear system identification](https://mlsanity.com/paper/1905.00820/) (2019)
- [Identification of block-oriented nonlinear systems starting from linear approximations: A survey](https://mlsanity.com/paper/1607.01217/) (2016)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Deep Identification of Nonlinear Systems in Koopman Form](https://mlsanity.com/paper/2110.02583/) (2021)
- [On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation](https://mlsanity.com/paper/2004.05040/) (2020)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (2021)
- [Non-linear State-space Model Identification from Video Data using Deep Encoders](https://mlsanity.com/paper/2012.07721/) (2020)
- [Deep-Learning-Based Identification of LPV Models for Nonlinear Systems](https://mlsanity.com/paper/2204.04060/) (2022)

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

- [Orthogonal projection-based regularization for efficient model augmentation](https://mlsanity.com/paper/2501.05842/) (2025)

## Abstract (arXiv)

The SUBNET neural network architecture has been developed to identify nonlinear state-space models from input-output data. To achieve this, it combines the rolled-out nonlinear state-space equations and a state encoder function, both parameterised as neural networks The encoder function is introduced to reconstruct the current state from past input-output data. Hence, it enables the forward simulation of the rolled-out state-space model. While this approach has shown to provide high-accuracy and consistent model estimation, its convergence can be significantly improved by efficient initialization of the training process. This paper focuses on such an initialisation of the subspace encoder approach using the Best Linear Approximation (BLA). Using the BLA provided state-space matrices and its associated reconstructability map, both the state-transition part of the network and the encoder are initialized. The performance of the improved initialisation scheme is evaluated on a Wiener-Hammerstein simulation example and a benchmark dataset. The results show that for a weakly nonlinear system, the proposed initialisation based on the linear reconstructability map results in a faster convergence and a better model quality.