# Online Real-time Learning of Dynamical Systems from Noisy Streaming Data: A Koopman Operator Approach

arXiv: https://arxiv.org/abs/2212.05259 · HTML: https://mlsanity.com/paper/2212.05259/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 10 Dec 2022.

## Builds on (most cited first, 15 of 15)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control](https://mlsanity.com/paper/1902.02827/) (2019)
- [On Robust Computation of Koopman Operator and Prediction in Random Dynamical Systems](https://mlsanity.com/paper/1803.08562/) (2018)
- [Applied Koopman Operator Theory for Power Systems Technology](https://mlsanity.com/paper/1706.00159/) (2017)
- [Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis](https://mlsanity.com/paper/2106.15678/) (2021)
- [Graph Neural Network and Koopman Models for Learning Networked Dynamics: A Comparative Study on Power Grid Transients Prediction](https://mlsanity.com/paper/2202.08065/) (2022)
- [Feedback Stabilization Using Koopman Operator](https://mlsanity.com/paper/1810.00089/) (2018)
- [Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modes](https://mlsanity.com/paper/2007.11717/) (2020)
- [On Information Transfer Based Characterization of Power System Stability](https://mlsanity.com/paper/1809.07704/) (2018)
- [Data-Driven Operator Theoretic Methods for Global Phase Space Learning](https://mlsanity.com/paper/1910.03011/) (2019)
- [Data Driven Online Learning of Power System Dynamics](https://mlsanity.com/paper/2003.05068/) (2020)
- [Data-driven Stabilization of Discrete-time Control-affine Nonlinear Systems: A Koopman Operator Approach](https://mlsanity.com/paper/2203.14114/) (2022)
- [Pulse-Based Control Using Koopman Operator Under Parametric Uncertainty](https://mlsanity.com/paper/1708.00232/) (2017)

## Built on by (most cited first, 3 of 3)

- [Streaming Operator Inference for Model Reduction of Large-Scale Dynamical Systems](https://mlsanity.com/paper/2601.12161/) (2026)
- [Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD](https://mlsanity.com/paper/2408.06607/) (2024)
- [Conformal Online Learning of Deep Koopman Linear Embeddings](https://mlsanity.com/paper/2511.12760/) (2025)

## Abstract (arXiv)

Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: a) it allows for online real-time monitoring of a dynamical system; b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; c) it is computationally fast and less intensive than the popular Extended Dynamic Mode Decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.