# Online learning of neural state-space models

arXiv: https://arxiv.org/abs/2607.17614 · HTML: https://mlsanity.com/paper/2607.17614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Deep Identification of Nonlinear Systems in Koopman Form](https://mlsanity.com/paper/2110.02583/) (2021)
- [An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularization](https://mlsanity.com/paper/2403.03827/) (2024)
- [On the adaptation of in-context learners for system identification](https://mlsanity.com/paper/2312.04083/) (2023)
- [Deep-Learning-Based Identification of LPV Models for Nonlinear Systems](https://mlsanity.com/paper/2204.04060/) (2022)
- [Efficient identification of linear, parameter-varying, and nonlinear systems with noise models](https://mlsanity.com/paper/2504.11982/) (2025)
- [Data-driven augmentation of first-principles models under constraint-free well-posedness and stability guarantees](https://mlsanity.com/paper/2604.11421/) (2026)
- [Online Learning of Nonlinear Parametric Models under Non-smooth Regularization using EKF and ADMM](https://mlsanity.com/paper/2503.01282/) (2025)
- [Learning-based augmentation of first-principle models: A linear fractional representation-based approach](https://mlsanity.com/paper/2602.17297/) (2026)

## Abstract (arXiv)

Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data. These methods are typically used in multiple-shooting-based offline identification, and online learning of these models remains largely unexplored. This paper presents a batch-wise learning pipeline and a direct recursive identification algorithm for subspace encoder-based ANN-SS models. We provide convergence analysis of the recursive formulation and validate its performance through extensive simulation studies. The results demonstrate that the proposed approach enables computationally efficient online adaptation with high model accuracy.