# Nonlinear System Identification: A User-Oriented Roadmap

arXiv: https://arxiv.org/abs/1902.00683 · HTML: https://mlsanity.com/paper/1902.00683/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2019.

## Built on by (most cited first, 30 of 57)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
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- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Constrained Block Nonlinear Neural Dynamical Models](https://mlsanity.com/paper/2101.01864/) (2021)
- [Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networks](https://mlsanity.com/paper/2404.12416/) (2024)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (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)
- [Baseline Results for Selected Nonlinear System Identification Benchmarks](https://mlsanity.com/paper/2405.10779/) (2024)
- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions](https://mlsanity.com/paper/2206.05183/) (2022)
- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)
- [Model order reduction of deep structured state-space models: A system-theoretic approach](https://mlsanity.com/paper/2403.14833/) (2024)
- [Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2305.01338/) (2023)
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- [On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamics](https://mlsanity.com/paper/2201.00384/) (2022)
- [Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States](https://mlsanity.com/paper/2303.17963/) (2023)
- [Stable Inverse Reinforcement Learning: Policies from Control Lyapunov Landscapes](https://mlsanity.com/paper/2405.08756/) (2024)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Piecewise linear regression and classification](https://mlsanity.com/paper/2103.06189/) (2021)
- [An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models](https://mlsanity.com/paper/2203.16290/) (2022)
- [Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamics](https://mlsanity.com/paper/2209.12489/) (2022)
- [Efficient identification of linear, parameter-varying, and nonlinear systems with noise models](https://mlsanity.com/paper/2504.11982/) (2025)
- [NARX Identification using Derivative-Based Regularized Neural Networks](https://mlsanity.com/paper/2204.05892/) (2022)
- [Decoupling multivariate functions using a nonparametric filtered tensor decomposition](https://mlsanity.com/paper/2205.11153/) (2022)
- [Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning](https://mlsanity.com/paper/2205.15703/) (2022)
- [Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification](https://mlsanity.com/paper/2212.13902/) (2022)

## Abstract (arXiv)

The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear dynamic systems. In addition, the article also provides a broad perspective on the topic to researchers that are already familiar with the linear system identification theory, showing the similarities and differences between the linear and nonlinear problem. The reader will be referred to the existing literature for detailed mathematical explanations and formal proofs. Here the focus is on the basic philosophy, giving an intuitive understanding of the problems and the solutions, by making a guided tour along the wide range of user choices in nonlinear system identification. Guidelines will be given in addition to many examples, to reach that goal.