mlsanityData to 7 Oct 2026

Dynamic mode decomposition with control

arXiv 1409.6358 ↗First posted 22 Sep 2014math.OCcited by 128

Not on the map. Why?

Abstract (arXiv)

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations, only snapshots of state and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high-dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).

Key facts. Cited by 128 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Sep 2014.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 22; 2023: 26; 2024: 26; 2025: 18; 2026: 25.

128 papers.

Sort:

By area:

  1. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 110
  2. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 36
  3. 2022Residual Dynamic Mode Decomposition: Robust and verified Koopmanismcited by 36
  4. 2021Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantificationcited by 30
  5. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  6. 2022The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systemscited by 21
  7. 2023Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learningcited by 21
  8. 2023RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operatorcited by 17
  9. 2023Learning invariant representations of time-homogeneous stochastic dynamical systemscited by 17
  10. 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 16
  11. 2022Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamicscited by 16
  12. 2023Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systemscited by 11
38 more
  1. 2024Koopman-Assisted Reinforcement Learningcited by 11
  2. 2022Predicting the temporal dynamics of turbulent channels through deep learningcited by 10
  3. 2023PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operatorcited by 10
  4. 2023Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inferencecited by 10
  5. 2023Task-Oriented Koopman-Based Control with Contrastive Encodercited by 8
  6. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  7. 2022Comparative analysis of machine learning methods for active flow controlcited by 6
  8. 2022Deep Kernel Learning of Dynamical Models from High-Dimensional Noisy Datacited by 6
  9. 2022Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectoriescited by 6
  10. 2023Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshotscited by 6
  11. 2023Equivariance and partial observations in Koopman operator theory for partial differential equationscited by 6
  12. 2021On the Universal Transformation of Data-Driven Models to Control Systemscited by 5
  13. 2021CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixelscited by 5
  14. 2021Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamicscited by 5
  15. 2023Learning a model is paramount for sample efficiency in reinforcement learning control of PDEscited by 5
  16. 2023Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensemblescited by 5
  17. 2023Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Datacited by 5
  18. 2025Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networkscited by 5
  19. 2026LpWM: A Case for Sparse Representations in World Modelscited by 5
  20. 2021Stochastic Adversarial Koopman Model for Dynamical Systemscited by 4
  21. 2024Model-based deep reinforcement learning for accelerated learning from flow simulationscited by 4
  22. 2024Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order modelscited by 4
  23. 2025InputDSA: Demixing then Comparing Recurrent and Externally Driven Dynamicscited by 4
  24. 2022Context-aware controller inference for stabilizing dynamical systems from scarce datacited by 3
  25. 2022Design of a Supervisory Control System for Autonomous Operation of Advanced Reactorscited by 3
  26. 2023Data-Driven Model Reduction and Nonlinear Model Predictive Control of an Air Separation Unit by Applied Koopman Theorycited by 3
  27. 2024Correlating Time Series with Interpretable Convolutional Kernelscited by 3
  28. 2024Online Control-Informed Learningcited by 3
  29. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  30. 2024Analysis, forecasting and system identification of a floating offshore wind turbine using dynamic mode decompositioncited by 3
  31. 2025Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modelingcited by 3
  32. 2025Latent Twinscited by 3
  33. 2026Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Predictioncited by 3
  34. 2021Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEscited by 2
  35. 2021Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representationscited by 2
  36. 2021System Norm Regularization Methods for Koopman Operator Approximationcited by 2
  37. 2022Learning Deep Input-Output Stable Dynamicscited by 2
  38. 2022Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspacescited by 2

50 most cited of 128 All 128 (JSON)