Koopman Operator Learning

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Overview

Koopman operator learning represents a nonlinear system through observables whose evolution is linear, making forecasting and control easier to analyze and compute. Methods range from dynamic mode decomposition and extended DMD (EDMD) with fixed or learned dictionaries to kernel and reservoir methods, neural Koopman autoencoders, and structured continuous-time generators. Researchers test these models on chaotic and fluid systems, time-series benchmarks, and robots, often pairing them with model predictive control or reinforcement learning. A central challenge is balancing expressive learned representations with reliable spectra, stable long-horizon predictions, and guarantees under noise, limited data, or changing dynamics.

Latest papers

CardsList

82 papers10 papers in the last four weeks, up 67% on the four weeks before. 0.1% of all new papers.

  1. 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

  2. Extraction of linearized models from pre-trained networks via knowledge distillation

    Apr 8, 2026Fumito Kimura, Jun OhkuboKoopman Operator LearningImage Classification

    Graduate School of Science and Engineering, Saitama University, Sakura, Saitama, 338–8570 Japan

  3. RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments

    Apr 5, 2026Sriram S. K. S. Narayanan, Umesh VaidyaModel Predictive ControlQuadruped Locomotion

    Department of Mechanical Engineering, Clemson University, Clemson, SC 29630, USA

  4. 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.

  5. 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.

  6. NeuroBRIDGE: Behavior-Conditioned Koopman Dynamics with Riemannian Alignment for Early Substance Use Initiation Prediction from Longitudinal Functional Connectome

    Mar 31, 2026Badhan Mazumder, Sir-Lord Wiafe, Vince D. Calhoun +1Human Behavior PredictionFunctional Connectivity

    Department of Computer Science, Georgia State University · Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, and Emory University

  7. 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

  8. Koopman Operator Framework for Modeling and Control of Off-Road Vehicle on Deformable Terrain

    Mar 30, 2026Kartik Loya, Phanindra TallapragadaTerrain-Aware Robot LocomotionVehicle Dynamics

    Department of Mechanical Engineering, Clemson University, Clemson, SC 29607 USA

  9. Koopman Operator Identification of Model Parameter Trajectories for Temporal Domain Generalization (KOMET)

    Mar 27, 2026Randy C. Hoover, Jacob James, Paul May +1Extended Dynamic Mode DecompositionDrifting Models

    Department of Electrical Engineering and Computer Science (EECS), South Dakota Mines, Rapid City, SD 57702, USA · Data Science and Engineering Program within EECS, South Dakota Mines, Rapid City, SD 57702, USA · Department of Mathematics, South Dakota Mines, Rapid City, SD 57702, USA

  10. Automatic feature identification in least-squares policy iteration using the Koopman operator framework

    Mar 27, 2026Christian Mugisho Zagabe, Sebastian PeitzRL ControlPolicy Iteration

    Department of Computer Science & Lamarr Institute, TU Dortmund University, Germany

  11. 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

  12. Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds

    Mar 16, 2026Gustav Conradie, Nicolas Boullé, Jean-Christophe Loiseau +2Koopman Operator LearningUncertainty Quantification

    Centre for Mathematical Sciences, University of Cambridge, UK · Department of Mathematics, Imperial College London, UK · Laboratoire DynFluid, Arts et Métiers Institute of Technology, France +1

  13. Factorized Neural Implicit DMD for Parametric Dynamics

    Mar 11, 2026Siyuan Chen, Zhecheng Wang, Yixin Chen +4Dynamical SystemsNeural Surrogate Modeling

    Department of Computer Science, University of British Columbia, Vancouver, Canada · Department of Computer Science, University of Toronto, Toronto, Canada

  14. Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

    Mar 9, 2026Sucheta Ghosh, Zahra MonfaredElectrocardiogram ClassificationTime Series Transformers

    Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany · Department of Mathematics and Computer Science, Heidelberg University, Heidelberg, Germany · Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany

  15. Koopman Regularized Deep Speech Disentanglement for Speaker Verification

    Mar 5, 2026Nikos Chazaridis, Mohammad Belal, Rafael Mestre +2Speaker VerificationSpeaker Disentanglement

    School of Electronics and Computer Science, University of Southampton, SO17 1BJ Southampton, U.K. · Marine Geosciences, National Oceanography Centre, SO14 3ZH Southampton, U.K.

  16. Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach

    Mar 5, 2026Rares Grozavescu, Pengyu Zhang, Mark Girolami +1Spatiotemporal ForecastingPDE Surrogate Modeling

    Department of Engineering, University of Cambridge, Cambridge, UK · Alan Turing Institute, London, UK · INRIA, Paris, France

  17. Modeling and Control of a Pneumatic Soft Robotic Catheter Using Neural Koopman Operators

    Mar 4, 2026Yiyao Yue, Noah Barnes, Lingyun Di +4Robotic Endovascular InterventionContinuum Robot Control

    Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA. · Department of Mechanical Engineering, University of Maryland, College Park, MD, USA.

  18. Whole-Body Safe Control of Robotic Systems with Koopman Neural Dynamics

    Mar 4, 2026Sebin Jung, Abulikemu Abuduweili, Jiaxing Li +1Robotic ControlRobot Safety

    Robotics Institute, Carnegie Mellon University, Pittsburgh, PA.

  19. Scaling Law of Neural Koopman Operators

    Feb 23, 2026Abulikemu Abuduweili, Yuyang Pang, Feihan Li +1Koopman Operator LearningRobot Dynamics Learning

    Authors are with the Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

  20. Spatially Aware Dictionary-Free Koopman Eigenfunction Identification for Modeling and Control

    Nov 27, 2025David GrasevKoopman Operator LearningNonlinear System Identification

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

  21. Adversarial dynamical systems characterize when data-driven learning succeeds or fails

    Jul 8, 2024Matthew J. Colbrook, Igor Mezić, Alexei StepanenkoKoopman Operator LearningSpectral Methods

    DAMTP, University of Cambridge, Cambridge, CB3 0WA, UK. · University of California, Santa Barbara, CA 93106, USA.

  22. Nonparametric Control Koopman Operators

    May 12, 2024Petar Bevanda, Bas Driessen, Lucian Cristian Iacob +3Koopman Operator LearningSystem Identification

    Chair of Information-oriented Control, TU München, Germany · Control Systems Group, TU/e, Eindhoven, The Netherlands · Systems and Control Laboratory, HUNREN Institute for Computer Science and Control, Budapest, Hungary +2