# An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularization

arXiv: https://arxiv.org/abs/2403.03827 · HTML: https://mlsanity.com/paper/2403.03827/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 11 of 11)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [Gradient Sampling Methods for Nonsmooth Optimization](https://mlsanity.com/paper/1804.11003/) (2018)
- [Forward-backward quasi-Newton methods for nonsmooth optimization problems](https://mlsanity.com/paper/1604.08096/) (2016)
- [Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering](https://mlsanity.com/paper/2111.02673/) (2021)
- [Training Recurrent Neural Networks by Sequential Least Squares and the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2112.15348/) (2021)
- [A Levenberg-Marquardt Method for Nonsmooth Regularized Least Squares](https://mlsanity.com/paper/2301.02347/) (2023)

## Built on by (most cited first, 8 of 8)

- [Manifold meta-learning for reduced-complexity neural system identification](https://mlsanity.com/paper/2504.11811/) (2025)
- [Efficient identification of linear, parameter-varying, and nonlinear systems with noise models](https://mlsanity.com/paper/2504.11982/) (2025)
- [Parametric Nonconvex Optimization via Convex Surrogates](https://mlsanity.com/paper/2604.05640/) (2026)
- [Space-Filling Regularization for Robust and Interpretable Nonlinear State Space Models](https://mlsanity.com/paper/2507.07792/) (2025)
- [A proximal augmented Lagrangian method for nonconvex optimization with equality and inequality constraints](https://mlsanity.com/paper/2509.02894/) (2025)
- [A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures](https://mlsanity.com/paper/2605.14489/) (2026)
- [Online learning of neural state-space models](https://mlsanity.com/paper/2607.17614/) (2026)
- [Simpler Methods Work Better for L1 Penalized Logistic Models and Large Datasets](https://mlsanity.com/paper/2609.23995/) (2026)

## Abstract (arXiv)

In this paper, we propose a very efficient numerical method based on the L-BFGS-B algorithm for identifying linear and nonlinear discrete-time state-space models, possibly under ℓ1 and group-Lasso regularization for reducing model complexity. For the identification of linear models, we show that, compared to classical linear subspace methods, the approach often provides better results, is much more general in terms of the loss and regularization terms used (such as penalties for enforcing system stability), and is also more stable from a numerical point of view. The proposed method not only enriches the existing set of linear system identification tools but can also be applied to identifying a very broad class of parametric nonlinear state-space models, including recurrent neural networks. We illustrate the approach on synthetic and experimental datasets and apply it to solve a challenging industrial robot benchmark for nonlinear multi-input/multi-output system identification. A Python implementation of the proposed identification method is available in the package jax-sysid, available at https://github.com/bemporad/jax-sysid.