# Online Learning of Dynamical Systems: An Operator Theoretic Approach

arXiv: https://arxiv.org/abs/1909.12520 · HTML: https://mlsanity.com/paper/1909.12520/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Conformal Online Learning of Deep Koopman Linear Embeddings](https://mlsanity.com/paper/2511.12760/) (2025)

## Abstract (arXiv)

In this paper, we provide an algorithm for online computation of Koopman operator in real-time using streaming data. In recent years, there has been an increased interest in data-driven analysis of dynamical systems, with operator theoretic techniques being the most popular. Existing algorithms, like Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD), use the entire data set for computation of the Koopman operator. However, many real life applications like power system analysis, biological systems, building systems etc. requires the real-time computation and updating of the Koopman operator, as new data streams in. In this paper, we propose an iterative algorithm for online computation of Koopman operator such that at each time step the Koopman operator is updated incrementally. In particular, we propose a Recursive Extended Dynamic Decomposition (rEDMD) algorithm for computation of Koopman operator from streaming data. Further, we test the algorithm in three different dynamical systems, namely, a linear system, a nonlinear system and a system governed by a Partial Differential Equation (PDE) and illustrate the computational efficiency of the iterative algorithm over the existing DMD and EDMD algorithms.