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Nonlinear System Identification: A User-Oriented Roadmap

arXiv 1902.00683 ↗First posted 2 Feb 2019eess.SY cs.SYcited by 55

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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.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Feb 2019.

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Citing papers per year: 2021: 8; 2022: 10; 2023: 14; 2024: 10; 2025: 10; 2026: 3.

55 papers.

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  1. 2023Deep networks for system identification: a Surveycited by 35
  2. 2023Optimistic Active Exploration of Dynamical Systemscited by 32
  3. 2021Stochastic Physics-Informed Neural Ordinary Differential Equationscited by 19
  4. 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
  5. 2023A spectrum of physics-informed Gaussian processes for regression in engineeringcited by 13
  6. 2022Deep Subspace Encoders for Nonlinear System Identificationcited by 12
  7. 2021Constrained Block Nonlinear Neural Dynamical Modelscited by 9
  8. 2024Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networkscited by 9
  9. 2021Improved Initialization of State-Space Artificial Neural Networkscited by 8
  10. 2024An L-BFGS-B approach for linear and nonlinear system identification under ℓ1 and group-Lasso regularizationcited by 8
  11. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  12. 2022GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductionscited by 7
38 more
  1. 2024Baseline Results for Selected Nonlinear System Identification Benchmarkscited by 7
  2. 2024Model order reduction of deep structured state-space models: A system-theoretic approachcited by 6
  3. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 6
  4. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
  5. 2023Structured state-space models are deep Wiener modelscited by 4
  6. 2021Data-driven Aerodynamic Analysis of Structures using Gaussian Processescited by 3
  7. 2022On the effectiveness of Randomized Signatures as Reservoir for Learning Rough Dynamicscited by 3
  8. 2023Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent Statescited by 3
  9. 2021Piecewise linear regression and classificationcited by 2
  10. 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
  11. 2022Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamicscited by 2
  12. 2024Stable Inverse Reinforcement Learning: Policies from Control Lyapunov Landscapescited by 2
  13. 2024Combining Federated Learning and Control: A Surveycited by 2
  14. 2025Efficient identification of linear, parameter-varying, and nonlinear systems with noise modelscited by 2
  15. 2022NARX Identification using Derivative-Based Regularized Neural Networkscited by 1
  16. 2022Decoupling multivariate functions using a nonparametric filtered tensor decompositioncited by 1
  17. 2022Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learningcited by 1
  18. 2022Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identificationcited by 1
  19. 2023Deep active learning for nonlinear system identificationcited by 1
  20. 2023Initialization Approach for Nonlinear State-Space Identification via the Subspace Encoder Approachcited by 1
  21. 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
  22. 2024Identifiability of Differential-Algebraic Systemscited by 1
  23. 2024Identification For Control Based on Neural Networks: Approximately Linearizable Modelscited by 1
  24. 2025Orthogonal projection-based regularization for efficient model augmentationcited by 1
  25. 2025Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flowscited by 1
  26. 2025Optimal Bayesian Affine Estimator and Active Learning for the Wiener Modelcited by 1
  27. 2026Controller Design for Structured State-space Models via Contraction Theorycited by 1
  28. 2021PAMELI: A Meta-Algorithm for Computationally Expensive Multi-Objective Optimization Problemscited by 0
  29. 2021COSMIC: fast closed-form identification from large-scale data for LTV systemscited by 0
  30. 2023A critical look at deep neural network for dynamic system modelingcited by 0
  31. 2023Learning Flow Functions from Data with Applications to Nonlinear Oscillatorscited by 0
  32. 2023Autoregressive models for biomedical signal processingcited by 0
  33. 2023Orthogonal Transforms in Neural Networks Amount to Effective Regularizationcited by 0
  34. 2023Exploiting the capacity of deep networks only at training stage for nonlinear black-box system identificationcited by 0
  35. 2024State Derivative Normalization for Continuous-Time Deep Neural Networkscited by 0
  36. 2024A neural network-based approach to hybrid systems identification for controlcited by 0
  37. 2025An Iterative Bayesian Approach for System Identification based on Linear Gaussian Modelscited by 0
  38. 2025Subgradient Method for System Identification with Non-Smooth Objectivescited by 0

50 most cited of 55 All 55 (JSON)