Nonlinear System Identification

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Overview

The field seeks to recover how a system changes over time from measurements, so its behavior can be explained, predicted, or controlled. Approaches include sparse equation discovery such as SINDy and symbolic regression, Koopman and kernel methods, and neural state-space or differential-equation models; many incorporate physical structure such as energy conservation or dissipation. Methods are tested on settings ranging from chaotic ODEs and oscillators to robots, vehicles, and industrial processes, often with sparse, noisy, or partially observed data. A central challenge is that good predictions on observed trajectories do not guarantee that the model is identifiable, stable over long horizons, or reliable outside the training conditions.

Latest papers

CardsList

162 papers14 papers in the last four weeks, up 75% on the four weeks before. 0.1% of all new papers.

  1. xFODE: An Explainable Fuzzy Additive ODE Framework for System Identification

    Apr 16, 2026Ertugrul Kececi, Tufan KumbasarInterpretable MLNonlinear System Identification

    AI and Intelligent Systems Laboratory, Istanbul Technical University, 34469, Istanbul, Türkiye

  2. SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems

    Apr 16, 2026Murat Furkan Mansur, Tufan KumbasarNeural Surrogate ModelingParameter Estimation

    AI and Intelligent Systems Laboratory, Istanbul Technical University, 34469, Istanbul, Türkiye

  3. Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems

    Apr 14, 2026Binh Nguyen, Nam T. Nguyen, Truong X. NghiemPort-Hamiltonian SystemsHamiltonian Neural Networks

    Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA

  4. Tensor-based computation of the Koopman generator via operator logarithm

    Apr 9, 2026Tatsuya Kishimoto, Jun OhkuboKoopman Operator LearningNonlinear System Identification

    Graduate School of Science and Engineering, Saitama University 255 Shimo-Okubo, Sakura-ku, Saitama 338–8570, Japan

  5. A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data

    Apr 7, 2026Matteo Bosso, Giovanni Franzese, Kushal Swamy +3Nonlinear System IdentificationSymbolic Regression

  6. PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network

    Apr 7, 2026Achraf El Messaoudi, Karim Cherifi, Yann Le Gorrec +1Nonlinear System IdentificationPort-Hamiltonian Systems

    UMLP, ENSMM, FEMTO-ST · Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST, F-25000 Besançon, France

  7. A Robust SINDy Autoencoder for Noisy Dynamical System Identification

    Apr 6, 2026Kairui DingNonlinear System IdentificationSystem Identification

    Department of Mathematics, Columbia University

  8. Identification and Inference in Nonlinear Dynamic Network Models

    Apr 3, 2026Diego VallarinoParameter IdentifiabilityNonlinear System Identification

    Inter-American Development Bank (IDB), Washington, DC, United States

  9. On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations

    Apr 3, 2026Santosh Mohan Rajkumar, Dibyasri Barman, Kumar Vikram Singh +1Extended Dynamic Mode DecompositionDynamical Systems

    Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA. · Department of Chemical, Paper, and Biomedical Engineering at Miami University, Oxford, OH, USA. · Department of Mechanical and Manufacturing Engineering at Miami University, Oxford, OH, USA.

  10. Learning interacting particle systems from unlabeled data

    Apr 2, 2026Viska Wei, Fei LuSystem IdentificationNonlinear System Identification

    Department of Applied Mathematics and Statistics and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA. · Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA.

  11. Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine

    Apr 2, 2026David GrasevAdaptive MPCExtended Dynamic Mode Decomposition

    Department of Aviation Technology, University of Defence, Brno, Czech Republic.

  12. Predicting Dynamics of Ultra-Large Complex Systems by Inferring Governing Equations

    Apr 1, 2026Qi Shao, Duxin Chen, Jiawen Chen +5Dynamical SystemsNonlinear System Identification

    School of Mathematics, Southeast University, Nanjing, 210096, P. R. China. · School of Electronic Engineering and Computer Science, Queen Mary University of London, London, E1 4NS, UK. · School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK. +4

  13. Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

    Mar 31, 2026Simone Betteti, Luca LaurentiEnergy-Based ModelsDynamical Systems

    RIAS Lab, The Italian Institute of Artificial Intelligence for Industry, Turin, 10129, IT · Delft Center for Systems and Control, TU Delft, Delft, 2600 AA, The Netherlands

  14. Learning Surrogate LPV State-Space Models with Uncertainty Quantification

    Mar 31, 2026E. Javier Olucha, Amritam Das, Roland TóthSurrogate ModelingState Space Models

    Control Systems Group, Eindhoven University of Technology, The Netherlands · Systems and Control Laboratory, HUN-REN Institute for Computer Science and Control, Hungary

  15. Lie Generator Networks for Nonlinear Partial Differential Equations

    Mar 31, 2026Shafayeth Jamil, Rehan KapadiaKoopman Operator LearningPDE Operator Learning

    Ming Hsieh Department of Electrical and Computer Engineering University of Southern California

  16. Physics-Informed Neural Networks and Sequence Encoder: Application to heating and early cooling of thermo-stamping process

    Mar 27, 2026Mouad Elaarabi, Domenico Borzacchiello, Philippe Le Bot +2Physics-Informed MLNeural Surrogate Modeling

    Nantes Université, Ecole Centrale Nantes, CNRS, GeM, UMR 6183, Nantes, 44321, France · Nantes Université, IRT Jules Verne, Bouguenais, 44340, France

  17. Identifiability and amortized inference limitations in Kuramoto models

    Mar 23, 2026Emma Hannula, Jana de Wiljes, Matthew T. Moores +2Kuramoto ModelAmortized Inference

    LUT University, Yliopistonkatu 34, Lappeenranta, 53850, Finland · TU Ilmenau, Ehrenbergstraße 29, Ilmenau, 98693, Germany · University of Cambridge, Herschel Road, Cambridge, CB3 9AL, United Kingdom

  18. SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

    Mar 19, 2026Amanda A. Howard, Nicholas Zolman, Bruno Jacob +2Nonlinear System IdentificationSparse Identification of Nonlinear Dynamics

    Pacific Northwest National Laboratory, Richland, WA 99354 · University of Washington, Seattle, WA 98195

  19. Physics-informed Deep Mixture-of-Koopmans Vehicle Dynamics Model with Dual-branch Encoder for Distributed Electric-drive Trucks

    Mar 18, 2026Jinyu Miao, Pu Zhang, Rujun Yan +8Vehicle DynamicsKoopman Operator Learning

    School of Vehicle and Mobility, and State Key Laboratory of Intelligent Green Vehicle and Mobility, Tsinghua University, Beijing, China · KargoBot Inc., Beijing, China

  20. Data-driven forced response analysis with min-max representations of nonlinear restoring forces

    Mar 17, 2026Akira Saito, Hiromu FujitaNonlinear System IdentificationDynamical Systems

    Department of Mechanical Engineering, Meiji University, Kawasaki, Kanagawa 214-8571, Japan.

  21. Deep Adaptive Model-Based Design of Experiments

    Mar 17, 2026Arno Strouwen, Sebastian Micluţa-CâmpeanuBayesian Experimental DesignNonlinear System Identification

    Strouwen Statistics, Hasselt, Belgium · Biosystems Department, KU Leuven, Belgium · JuliaHub, Massachusetts, USA +1

  22. Minimum-Action Learning: Energy-Constrained Symbolic Model Selection for Physical Law Identification from Noisy Data

    Mar 16, 2026Martin G. FraschScientific DiscoveryModel Selection

    Institute on Human Development and Disability, University of Washington, Seattle, WA 98195, USA · Health Stream Analytics, LLC, Seattle, WA, USA

  23. NanoBench: A Multi-Task Benchmark Dataset for Nano-Quadrotor System Identification, Control, and State Estimation

    Mar 10, 2026Syed Izzat Ullah, Jose BacaBenchmark DesignNonlinear System Identification

    Department of Engineering Texas A&M University-Corpus Christi, Corpus Christi, TX, USA

  24. Vision-Augmented On-Track System Identification for Autonomous Racing via Attention-Based Priors and Iterative Neural Correction

    Mar 10, 2026Zhiping Wu, Cheng Hu, Yiqin Wang +2Nonlinear System IdentificationVehicle Dynamics

    State Key Laboratory of Industrial, Zhejiang University, Hangzhou 310027, China

  25. Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics

    Mar 5, 2026Jay Raut, Daniel N. Wilke, Stephan SchmidtSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa · School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg, South Africa

  26. Physics-Embedded Neural ODEs for Learning Antagonistic Pneumatic Artificial Muscle Dynamics

    Feb 27, 2026Xinyao Wang, Jonathan RealmutoPneumatic ActuationSoft Pneumatic Actuators

    Dept. of Mechanical Engineering, University of California, Riverside, CA, USA

  27. PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

    Feb 20, 2026Shubham Bhardwaj, Chandrajit BajajTime Series ForecastingPort-Hamiltonian Systems

    Department of Computer Science, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA

  28. Wideband Power Amplifier Behavioral Modeling Using an Amplitude Conditioned LSTM

    Feb 17, 2026Abdelrahman Abdelsalam, You FeiNonlinear System IdentificationLong Short-Term Memory Networks

    School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

  29. Hybrid Model Predictive Control with Physics-Informed Neural Network for Satellite Attitude Control

    Feb 17, 2026Carlo Cena, Mauro Martini, Marcello ChiabergeSpacecraft Attitude DeterminationModel Predictive Control

    Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy

  30. Controlled oscillation modeling using port-Hamiltonian neural networks

    Feb 17, 2026Maximino Linares, Guillaume Doras, Thomas HéliePort-Hamiltonian SystemsHamiltonian Dynamics

    IRCAM, 1, place Igor-Stravinsky, 75004, Paris, France