# Online dynamic mode decomposition for time-varying systems

arXiv: https://arxiv.org/abs/1707.02876 · HTML: https://mlsanity.com/paper/1707.02876/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2017.

## Built on by (most cited first, 23 of 23)

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- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [Learning to Optimize with Dynamic Mode Decomposition](https://mlsanity.com/paper/2211.16268/) (2022)
- [Nonparametric Sparse Online Learning of the Koopman Operator](https://mlsanity.com/paper/2405.07432/) (2024)
- [Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems](https://mlsanity.com/paper/2601.12161/) (2026)
- [Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression](https://mlsanity.com/paper/2208.07767/) (2022)
- [Learning Nonautonomous Systems via Dynamic Mode Decomposition](https://mlsanity.com/paper/2306.15618/) (2023)
- [On Dominant Manifolds in Reservoir Computing Networks](https://mlsanity.com/paper/2604.05967/) (2026)
- [Local dynamic mode of Cognitive Behavioral Therapy](https://mlsanity.com/paper/2205.09752/) (2022)
- [Koopman Learning with Episodic Memory](https://mlsanity.com/paper/2311.12615/) (2023)
- [Nonparametric Sparse Online Learning of the Koopman Operator](https://mlsanity.com/paper/2501.16489/) (2025)
- [Online Meal Detection Based on CGM Data Dynamics](https://mlsanity.com/paper/2507.00080/) (2025)
- [Online Kernel Dynamic Mode Decomposition for Streaming Time Series Forecasting with Adaptive Windowing](https://mlsanity.com/paper/2510.15404/) (2025)
- [Real-Time Learning of Predictive Dynamic Obstacle Models for Robotic Motion Planning](https://mlsanity.com/paper/2511.00814/) (2025)
- [Conformal Online Learning of Deep Koopman Linear Embeddings](https://mlsanity.com/paper/2511.12760/) (2025)
- [Data-Driven Modeling and Correction of Vehicle Dynamics](https://mlsanity.com/paper/2512.00289/) (2025)
- [Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems](https://mlsanity.com/paper/2604.12103/) (2026)
- [Efficient Reinforcement Learning using Linear Koopman Dynamics for Nonlinear Robotic Systems](https://mlsanity.com/paper/2604.19980/) (2026)
- [AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression](https://mlsanity.com/paper/2606.04930/) (2026)
- [Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis](https://mlsanity.com/paper/2609.04329/) (2026)

## Abstract (arXiv)

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data, and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of "windowed DMD", in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about~200, the proposed algorithm is the most efficient for real-time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.