Dynamic Mode Decomposition

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Dynamic Mode Decomposition studies how a system changes over time by fitting a linear operator to measured snapshots, yielding modes and growth rates that help explain and predict its dynamics. Extended and kernel DMD use richer observables to capture nonlinear behavior, while Hankel, optimized, and neural variants address limited data, noise, or complex spatial structure. Parametric and local methods aim to improve predictions across changing conditions, with applications ranging from fluid and structural systems to neural signals. A central challenge is that a model can fit short-term evolution well yet fail over long horizons or on unseen settings, making representation choice, robustness, and generalization active concerns.

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14 papers0 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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
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
Detecting high-frequency brain disorder signals using dynamic mode decomposition from EEG
Aug 3, 2026Jacob Kang, Jong-Hyeon SeoElectroencephalography Dynamic Mode Decomposition
Fischell Department of Bioengineering, University of Maryland, College Park, MD, United States · School of Basic Sciences, Hanbat National University, Daejeon, Republic of Korea
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
Cluster-Weighted EDMD
Jul 14, 2026Lorenzo Tomaz, Judd Rosenblatt, Flavio Kicis +2Koopman Operator Learning Latent Dynamics Modeling
AE Studio
SpatioTemporal Causal Network Diagnostics for Geographic Tipping Point Early Warning
Jun 16, 2026Zhaoyuan Yu, Zhangyong LiangChange-Point Detection Dynamic Mode Decomposition
Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China · National Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
Jun 3, 2026Kelan Gray, Finlay Brown, Nicolas Boullé +1Koopman Operator Learning Latent Dynamics Modeling
Department of Mathematics, Imperial College London, London, SW7 2AZ, UK. · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK.
Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework
May 14, 2026Cankat Tilki, Serkan GugercinDynamical Systems Koopman Operator Learning
Department of Mathematics, Virginia Tech, Blacksburg, VA - 24061.
Dynamic Mode Decomposition along Depth in Vision Transformers
May 8, 2026Nishant Suresh Aswani, Saif Eddin JabariTransformer Vision Transformer
NYU Tandon & NYU Abu Dhabi
Distributional Spectral Diagnostics for Localizing Grokking Transitions
May 7, 2026Ziyue Wang, Yufeng Ying, Takafumi KanamoriChange-Point Detection Grokking
Institute of Science Tokyo · University of Science and Technology of China
Equation-Free Digital Twins for Nonlinear Structural Dynamics
May 1, 2026Mohammad Mahdi Abaei, Ahmad BahooToroody, Arttu Polojärvi +4Koopman Operator Learning Nonlinear System Identification
Department of Mechanical Engineering, Marine Technology and Arctic Group, Aalto University, Finland · Independent Expert, Digital Twin Technology, Ribe, Denmark · Institute for Risk and Reliability, Leibniz University Hannover, Germany
Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems
Apr 13, 2026Ananda Chakrabarti, Haitham H. Saleh, Indranil Nayak +3Reduced-Order Modeling Dynamic Mode Decomposition
Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA · ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212, USA · SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025, USA +1
Factorized Neural Implicit DMD for Parametric Dynamics
Mar 11, 2026Siyuan Chen, Zhecheng Wang, Yixin Chen +4Dynamical Systems Neural Surrogate Modeling
Department of Computer Science, University of British Columbia, Vancouver, Canada · Department of Computer Science, University of Toronto, Toronto, Canada
NeuralDMD: Interpretable Neural Representation of Dynamics from Sparse and Noisy Measurements
Jul 3, 2025Ali SaraerToosi, Renbo Tu, Esther Y. H. Lin +2Spatiotemporal Forecasting Inverse Problems
University of Toronto, Toronto, ON, Canada · Vector Institute, Toronto, ON, Canada · NVIDIA Corporation, USA

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Functional dynamic mode decomposition: Learning infinite-dimensional systems from data

Stefan Klus, Eirini Ioannou

School of Mathematical & Computer Sciences, Heriot–Watt University, Edinburgh, UK · Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University, Edinburgh, UK

Koopman Operator Learning Dynamic Mode Decomposition

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Dynamic mode decomposition (DMD) is a data-driven method that computes the best linear approximation of the underlying dynamical system and decomposes the dynamics into a superposition of characteristic spatiotemporal patterns. Originally introduced by the fluid dynamics community, DMD and its extensions have found widespread use in many other research areas such as molecular dynamics, climate science, engineering, finance, and neuroscience. Applications include dimensionality reduction, forecasting, system identification, control, and spectral clustering. In order to apply DMD to partial differential equations, the spatial domain is typically first discretized using finite difference or finite element techniques, thus implicitly rendering the problem finite-dimensional. We extend projected and exact DMD to infinite-dimensional systems. Rather than estimating matrices from vector-valued observations, our DMD variants learn finite-rank operators from functional data such as observables, densities, or wavefunctions. We show that conventional DMD algorithms can be regarded as special cases of their functional DMD counterparts. All results will be illustrated with the aid of guiding examples. We focus in particular on Koopman, Perron-Frobenius, and Koopman-von Neumann operators associated with graphons, ordinary differential equations, and stochastic differential equations.