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. Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems

    Oct 29, 2026Ana Čukarska, Maximilian Gollwitzer, Viola Muning Li +3Koopman Operator LearningNonlinear System Identification

    School of Computation, Information and Technology, Technical University of Munich, Germany · Munich Data Science Institute · Interdisciplinary Center for Scientific Computing (IWR) +1

  2. Deep Bayesian Filtering for Nonlinear Structural System Identification: A Tutorial on Structural and Physical Inductive Biases

    Oct 27, 2026Wei Liu, Konstantinos Vlachas, Eleni ChatziSystem IdentificationNonlinear System Identification

    National University of Singapore Singapore · ETH Zurich Zurich, Switzerland

  3. Neural Closed-Loop Identification of Nonlinear Systems with Stability and Generalization Guarantees

    Oct 20, 2026Laura Meroi, Mahrokh G. Boroujeni, Leonardo Massai +1PAC-Bayesian TheoryNonlinear System Identification

    Institute of Mechanical Engineering, EPFL, Switzerland.

  4. Towards a GraphNARX model for structural dynamics

    Oct 16, 2026George Tsialiamanis, Keith WordenNonlinear System IdentificationTime Series Modeling

    Dynamics Research Group, School of Mechanical, Aerospace, and Civil Engineering, University of Sheffield, Sheffield, Mappin St, Sheffield, United Kingdom

  5. Learning smooth dynamics via Kinematic Interpolants

    Oct 15, 2026Yiheng, Jiang, Youssef Marzouk +2Dynamical SystemsNonlinear System Identification

    Roger · Massachusetts Institute of Technology. · Imperial College London and Mila – Québec AI Institute. +1

  6. Sequential Learning-Based Physics-Informed Neural Network Modeling for Parameter Estimation on a Power Converter

    Oct 14, 2026Samuela Rokocakau, Panagiotis Kakosimos, Giulia Tresca +1Parameter EstimationPhysics-Informed ML

    ABB Corporate Research Center, Väster˚as, Sweden · Dept. of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy

  7. Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements

    Oct 12, 2026Yibo Zhou, Johannes KöhlerNonlinear System IdentificationSystem Identification

    Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden · Department of Mechanical Engineering, Imperial College London, London, United Kingdom

  8. Dissipative Lagrangian Neural Networks for the Interpretable Modelling of Passive Mechanical Systems

    Oct 11, 2026Rob Seabourne, Alice CicirelloLagrangian Neural NetworksSystem Identification

    Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, UK

  9. In-Context Learning for System Identification: Probabilistic Formulation, Long-Sequence Handling, and Benchmark Validation

    Oct 9, 2026Matteo Rufolo, Dario Piga, Filippo Pura +1System IdentificationIn-Context Learning

    SUPSI, IDSIA - Dalle Molle Institute for Artificial Intelligence, Lugano, Switzerland · USI, Faculty of Informatics, Lugano, Switzerland

  10. Identifiability of a dissipative knowledge-dynamics model: exact recovery under designed excitation, degeneration on observational data

    Oct 7, 2026Arman Kostanian, Armen BeklaryanParameter IdentifiabilityNonlinear System Identification

    Innopolis University, Innopolis, Russia · HSE University, Moscow, Russia

  11. Attenuated in-context identification in time-series foundation models: diagnosis under counterfactual inputs and repair by synthetic forced-system fine-tuning

    Oct 6, 2026Hong-In WonNonlinear System IdentificationCounterfactual Prediction

    Manufacturing AI Research Center, Korea Institute of Industrial Technology, Incheon, Republic of Korea · HYU-KITECH Joint Department, Graduate School, Hanyang University, Seoul, Republic of Korea

  12. Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems

    Oct 3, 2026Anand Kumar Agrawal, Anders ThorinLagrangian Neural NetworksReduced-Order Modeling

    Université Paris-Saclay, CEA List, Palaiseau, France

  13. Learning Closure of Dynamical Systems with Kernel Ridge Regression

    Oct 1, 2026Evan Habbershaw, John Harlim, Senwei LiangPDE Surrogate ModelingNonlinear System Identification

    Department of Mathematics, The Pennsylvania State University · Department of Mathematics and Institute for Computational and Data Sciences, The Pennsylvania State University · Department of Mathematics and Statistics, Texas Tech University

  14. From Redundancy to Minimality: Fixed-Point-Guided Hierarchical Reduction of Learned Piecewise-Linear Dynamics

    Oct 1, 2026Hiroto Tamura, Gouhei TanakaDynamical SystemsNonlinear System Identification

    Graduate School of Informatics, Osaka Metropolitan University, Osaka, Japan · International Research Center for Neurointelligence (IRCN), The University of Tokyo, Tokyo, Japan · Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

  15. On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability

    Sep 30, 2026Wenjie Wang, Yuanyuan Wang, Zixiang Jiang +2Parameter EstimationParameter Identifiability

    University of Melbourne · Mohamed bin Zayed University of Artificial Intelligence · Carnegie Mellon University

  16. Information-theoretic receding-horizon active learning of nonlinear dynamical systems

    Sep 29, 2026Juncal Arbelaiz, Anushri Arora, Jonathan W. PillowActive LearningNonlinear System Identification

    Princeton Neuroscience Institute and Center for Statistics and Machine Learning, Princeton University · Computer Science Department, Princeton University

  17. Simulation-Free Learning of GP-SDEs from Irregular Observations

    Sep 27, 2026Zhidi Lin, Yuhao Liu, Ying Li +2Stochastic Differential EquationsState Space Models

    The University of Hong Kong · Capital One · National University of Singapore +1

  18. Equation discovery with Bayesian tree-adjoining grammars

    Sep 25, 2026Christopher A. Lindley, Nikolaos Dervilis, Keith WordenNonlinear System IdentificationScientific Discovery

    Dynamics Research Group University of Sheffield Mappin St, Sheffield, UK

  19. Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Data

    Sep 21, 2026Jule Budnick, Andrew Keane, Serhiy YanchukNonlinear System IdentificationReservoir Computing

    School of Mathematical Sciences, University College Cork, Cork, Ireland · Potsdam Institute for Climate Impact Research, Potsdam, Germany

  20. Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems

    Sep 16, 2026Yahya Sattar, Yassir Jedra, Robin Strässer +3Dynamical SystemsFeedback Control

    Cornell University · Imperial College London · University of Stuttgart +2

  21. Port-Hamiltonian Koopman Operator Synthesis for Mechanical Systems

    Sep 15, 2026Rajpal Singh, Aditya Singh, Jishnu KeshavanRobot Dynamics IdentificationKoopman Operator Learning

    Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India

  22. Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics

    Sep 8, 2026Will Houser, Vanja Dukic, David M. BortzSparse Identification of Nonlinear DynamicsNonlinear System Identification

    Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526 USA

  23. Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis

    Sep 3, 2026Seyyed Shaho Alaviani, Yongzhi Qu, Gregory W. VoglODE DiscoveryNonlinear System Identification

    Department of Mechanical Engineering University of Minnesota-Twin Cities Minneapolis, MN 55455, USA · Department of Mechanical Engineering University of Utah Salt Lake City, UT 84112, USA · National Institute of Standards and Technology Gaithersburg, MD 20899, USA

  24. A Hybrid PEM-GP Framework for Uncertainty-Aware System Identification of Quadcopters

    Aug 31, 2026Abdallah Ghoul, Ismail Khalil Bousserhane, Kadri BoufeldjaRobot Dynamics IdentificationNonlinear System Identification

    Electrical Engineering Department, University of Bechar, Bechar 08000, Algeria

  25. System Identification of Admittance Models for Large Real-World Objects

    Aug 30, 2026Nathan I. Baum, Nathaniel G. Luttmer, Mark A. MinorNonlinear System IdentificationHaptic Feedback

    Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112, USA

  26. Simultaneous inference of environmental and interaction forces in collective dynamics

    Aug 25, 2026Nipuni de Silva, Ming Zhong, James M. GreeneEmergent Behavior in Multi-Agent SystemsNonlinear System Identification

    Department of Mathematics, Clarkson University, Potsdam, NY, United States · Department of Mathematics, University of Houston, Houston, TX, United States

  27. Gaussian process learning with flow map refinement for parameter estimation in dynamical systems

    Aug 23, 2026Yue Hao, Dongwei YeParameter EstimationNonlinear System Identification

    School of Mathematical Science, Suzhou University of Science and Technology, Suzhou, PR China · Department of Applied Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, PR China

  28. Learning Reduced-Order Dynamics with Singularity via Latent-Augmented Neural Ordinary Differential Equations

    Aug 22, 2026Xiaorui Wang, Yu Zhou, Wenjie Mei +3Reduced-Order ModelingNeural ODEs

    Lanzhou University of Technology, School of Automation and Electrical Engineering, Lanzhou, 730050, Gansu, China · Hiroshima University, Graduate School of Advanced Science and Engineering, Higashihiroshima, 739-0046, Hiroshima, Japan · Nanjing University - Suzhou Campus, School of Robotics and Automation, Suzhou, 215163, Jiangsu, China +1

  29. Symbolic Neural ODEs: Learning interpretable models from time-series data

    Aug 22, 2026Nibodh Boddupalli, Jeff MoehlisNonlinear System IdentificationSystem Identification

    Dept. of Mechanical Engineering, University of California, Santa Barbara, CA 93106

  30. Learning piecewise-smooth dynamical systems

    Aug 20, 2026Davide Murari, Erik Jansson, Chris Budd OBE +1Dynamical SystemsRegime-Switching Dynamical Systems

    Department of Applied Mathematics and Theoretical Physics University of Cambridge · Department of Mathematical Sciences University of Bath