# Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control

arXiv: https://arxiv.org/abs/1911.08751 · HTML: https://mlsanity.com/paper/1911.08751/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 14 of 14)

- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Leveraging KANs For Enhanced Deep Koopman Operator Discovery](https://mlsanity.com/paper/2406.02875/) (2024)
- [Learning the Koopman Eigendecomposition: A Diffeomorphic Approach](https://mlsanity.com/paper/2110.07786/) (2021)
- [Learning spatio-temporal patterns with Neural Cellular Automata](https://mlsanity.com/paper/2310.14809/) (2023)
- [Online Estimation of the Koopman Operator Using Fourier Features](https://mlsanity.com/paper/2212.01503/) (2022)
- [Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control](https://mlsanity.com/paper/2309.04074/) (2023)
- [Deep Learning Based Dynamics Identification and Linearization of Orbital Problems using Koopman Theory](https://mlsanity.com/paper/2403.08965/) (2024)
- [Learning Linear Embeddings for Non-Linear Network Dynamics with Koopman Message Passing](https://mlsanity.com/paper/2305.09060/) (2023)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)
- [TRENDy: Temporal Regression of Effective Nonlinear Dynamics](https://mlsanity.com/paper/2412.03496/) (2024)
- [Adaptive Digital Twin of Sheet Metal Forming via Proper Orthogonal Decomposition-Based Koopman Operator with Model Predictive Control](https://mlsanity.com/paper/2511.10852/) (2025)
- [Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System](https://mlsanity.com/paper/2504.06818/) (2025)
- [partialCBDs: Differentiable Causal Block Diagrams](https://mlsanity.com/paper/2602.07581/) (2026)

## Abstract (arXiv)

This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear state-space model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.