Koopman Operator Learning

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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

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

Real-Time Disturbance-Aware Koopman Model Predictive Control for Quadrotors in Spatially Varying Winds
Oct 20, 2026Stella Kombo, Masih Haseli, Alejandro A. Stefan-Zavala +3Adaptive MPC Quadrotor Control
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA.
SALTO: Solver-Anchored Lifted Transfer Operators for Nonlinear Event Inference
Oct 15, 2026Qi Wang, Rylie FosterPDE Inverse Problems Koopman Operator Learning
Department of Aerospace Engineering San Diego State University San Diego, CA 92182, USA · Computational Science Research Center San Diego State University San Diego, CA 92182, USA · Department of Mechanical and Aerospace Engineering University of California, Irvine, CA 92697, USA
Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
Oct 8, 2026Joel-Pascal Ntwali N'konzi, Feliks Nüske, Stefan KlusExtended Dynamic Mode Decomposition Koopman Operator Learning
Maxwell Institute for Mathematical Sciences, The University of Edinburgh & Heriot–Watt University, Edinburgh, United Kingdom · Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany · LAAS-CNRS, Université de Toulouse, Toulouse, France +1
Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability
Oct 8, 2026Itsushi Sakata, Yuta Miyauchi, Yoshinobu KawaharaLatent Dynamics Modeling Dynamical Systems
RIKEN Center for Advanced Intelligence Project, Tokyo, Japan. · Graduate School of Information Science and Technology, The University of Osaka, Suita, Osaka, Japan.
Koopman Observers for Diffusion Acceleration: Correcting Feature Forecasts with Shallow Measurements
Oct 7, 2026Hanru Bai, Yuanchao Xu, Fengyi LiDiffusion Model Inference Acceleration Diffusion Model Caching
ETH Zurich · Max Planck Institute for Intelligent Systems · Kyoto University +1
Kapture: Capturing Cardiac Dynamics with Koopman-Governed Learning for Efficient Radar-Based Electrocardiogram Recovery
Oct 4, 2026Tong Wu, Jing Peng, Ziqi Feng +1Electrocardiography mmWave Radar Sensing
Amazon, Seattle, Washington, United States · Equitable, Waterloo, Canada · School of Psychology & Neuroscience, University of Glasgow, Glasgow, United Kingdom
Differentiable Koopman Operator for Contrastive Learning on Dynamic Graphs
Oct 2, 2026Md Abrar Jahin, Taufikur Rahman Fuad, Md Rizwan ParvezDynamic Graph Learning Graph SSL
University of Southern California · Islamic University of Technology · Qatar Computing Research Institute (QCRI)
Adaptive Spectral-Koopman Dynamics Modeling for Temporal Domain Generalization
Oct 2, 2026Tengxue Zhang, Yu Ke, Yang Shu +4Domain Generalization Koopman Operator Learning
East China Normal University · Chang’an University
Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecasting
Sep 29, 2026Anthony Frion, Lucas Drumetz, Guillaume Tochon +3Probabilistic Time Series Forecasting Long-Term Time Series Forecasting
Institute of coastal modelling Helmholtz-Zentrum Hereon · IMT Atlantique Lab-STICC, UMR CNRS 6285, Brest, France · LRE EPITA, Le Kremlin-Bicêtre, France +1
DisKO: Deep Koopman Learning in Distribution Space from Unpaired Snapshots
Sep 28, 2026He Ma, Xiaochen Liu, Wanfeng Lu +3Koopman Operator Learning Latent Dynamics Modeling
School of Mathematical Sciences, Fudan University, China. · Research Institute of Intelligent Complex Systems, Fudan University, China. · Shanghai Center for Mathematical Sciences, Fudan University, China. +2
KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots
Sep 27, 2026Wanfeng Lu, Yutong Zhang, Keyi Zhou +3Koopman Operator Learning Latent Dynamics Modeling
School of Mathematical Sciences, SCMS, SCAM, and CCSB, Fudan University, China · Research Institute of Intelligent Complex Systems, Fudan University, China · State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Brain Science, Fudan University, China +1
Prediction Limits and Koopman Closure of Geometry-Induced Soft State Abstractions
Sep 26, 2026Mohit Kumar, Somayeh KargaranKoopman Operator Learning State Abstraction
University of Rostock, Rostock, Germany · Software Competence Center Hagenberg, Hagenberg, Austria
Functional dynamic mode decomposition: Learning infinite-dimensional systems from data
Sep 24, 2026Stefan Klus, Eirini IoannouKoopman Operator Learning Dynamic Mode Decomposition
School of Mathematical & Computer Sciences, Heriot–Watt University, Edinburgh, UK · Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University, Edinburgh, UK
Principled Koopman Representations with Kalman Inference for Efficient Time-Series Prediction
Sep 15, 2026Ruiquan Li, Yuheng BuKoopman Operator Learning Time Series Forecasting
Department of Computer Science, UC Santa Barbara
Port-Hamiltonian Koopman Operator Synthesis for Mechanical Systems
Sep 15, 2026Rajpal Singh, Aditya Singh, Jishnu KeshavanRobot Dynamics Identification Koopman Operator Learning
Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
Learning Metastable Dynamics
Sep 13, 2026Rupak Majumdar, Mahmoud Salamati, Nikhil Singh +1Dynamical Systems Koopman Operator Learning
Max Planck Institute for Software Systems Germany · University of Birmingham, United Kingdom
Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems
Aug 29, 2026Aidan Li, Uday Kiran Reddy Tadipatri, Mahan Fathi +2Koopman Operator Learning Dynamical Systems
Chandar Research Lab · Mila – Quebec AI Institute · Université de Montréal +4
Data-driven Koopman mode approximation: A neural power iteration algorithm
Aug 27, 2026Guillaume O. Berger, Raphaël M. JungersKoopman Operator Learning Spectral Methods
ICTEAM, UCLouvain, Louvain-la-Neuve, Belgium
Using Composition Operators to Linearize LLM Semantic Transformations
Aug 25, 2026Afjal Chowdhury, James Chen, Alan EdelmanKoopman Operator Learning Representation Geometry in Language Models
Massachusetts Institute of Technology
FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization
Aug 23, 2026En Yu, Xiaoyu Yang, Wei Duan +2Domain Generalization Koopman Operator Learning
Australian Artificial Intelligence Institute (AAII), Faculty of Engineering and Information Technology, University of Technology Sydney (UTS), Australia
Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems
Aug 19, 2026Mark Kozdoba, Shie MannorDimensionality Reduction Koopman Operator Learning
Technion, IIT · Technion, IIT and NVIDIA
Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics
Aug 17, 2026Anima Kujur, Zahra MonfaredKoopman Operator Learning Dynamic Mode Decomposition
Interdisciplinary Centre for Scientific Computing (IWR) Heidelberg University, Heidelberg, Germany · Department of Mathematics and Computer Science Heidelberg University, Heidelberg, Germany
KOALA: Koopman Operator Learning for WiFi-Based Anticipatory Hum
Aug 16, 2026Quang-Anh N. D., Duc Pham Minh, Thao Phuong Pham +3Human Motion Prediction Wi-Fi Sensing
London Digital Twin Research Centre Middesex University · University of Arkansas · Agora Intelligence Lab
Koopman early warning signals for bifurcation and rate-induced tipping
Aug 12, 2026Juan Nathaniel, Carla Roesch, Derek DeSantis +5Early Warning Detection Dynamical Systems
Columbia University, USA · University of Edinburgh, UK · Los Alamos National Laboratory, USA +3
End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting
Aug 9, 2026De-Yan Lu, Xugang Lu, Yu Tsao +1Koopman Operator Learning Time Series Forecasting
Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan · National Institute of Information and Communications Technology, Kyoto, Japan · Research Center for Information Technology Innovation, Academic Sinica, Taipei, Taiwan
Dynamics-aware identification of governing equations from sparse and noisy data
Jul 31, 2026Pongpisit Thanasutives, Yoshinobu KawaharaKoopman Operator Learning Sparse Identification of Nonlinear Dynamics
Center for Advanced Intelligence Project (AIP), RIKEN, Osaka, Japan · 2Graduate School of Information Science and Technology, The University of Osaka, Osaka, Japan
MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts
Jul 28, 2026Mahmoud Selim, Sriharsha Bhat, Karl H. JohanssonUncertainty Quantification Koopman Operator Learning
TRATON · KTH Royal Institute of Technology
Learning Ergodic Dynamical Systems from a Finite Trajectory
Jul 24, 2026Oleksii Kachaiev, Silvia Villa, Lorenzo RosascoKoopman Operator Learning Markov Models
MaLGa center, DIMA, Università degli Studi di Genova, Genoa, Italy · Istituto Italiano di Tecnologia, Genoa, Italy · MaLGa center, DIBRIS, Università degli Studi di Genova, Genoa, Italy
Koopman Dreamer: Spectrally Constrained Latent Dynamics for Stable World-Model Imagination
Jul 22, 2026Jiaqi Li, Xinglong Zhang, Haibin Xie +3Koopman Operator Learning Latent Dynamics Modeling
College of Intelligence Science and Technology, National University of Defense Technology, Changsha, China
Koopman DCM: Unstable Eigenfunctions as Data-driven Representations for Legged Balancing
Jul 21, 2026Stéphane CaronLegged Robotics Koopman Operator Learning
Institute for Intelligent Systems and Robotics CNRS and Sorbonne University, Paris, France

Oct 20, 2026J/K move · Enter open · S save

Real-Time Disturbance-Aware Koopman Model Predictive Control for Quadrotors in Spatially Varying Winds

Stella Kombo, Masih Haseli, Alejandro A. Stefan-Zavala, Peter I. Renn+2

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA.

Adaptive MPC Quadrotor Control Koopman Operator Learning Model Predictive Control Disturbance Rejection Robot Dynamics Learning

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Reliable quadrotor flight in disturbed environments requires predictive models that remain accurate as unmodeled aerodynamic effects change during deployment. We introduce a disturbance-aware Koopman Control Family (DA-KCF) framework that preserves an offline-identified nominal model while learning only a disturbance-induced correction online. A reference-dependent KCF is first learned from simulation data and calibrated using limited hardware data. During deployment, the nominal KCF remains fixed while a lightweight residual ensemble learns a low-dimensional disturbance correction from causal state-command-state transitions. The Adaptive DA-KCF model is incorporated into MPC, where disturbance corrections are evaluated along the prediction horizon to optimize position and yaw references sent to the onboard stabilizing controller. Hardware experiments on a nano-quadrotor under uniform wind and a spatially varying wake demonstrate that online adaptation improves multi-step prediction and trajectory tracking as disturbance-induced model mismatch increases, while satisfying real-time control requirements.