# Deep Koopman Learning of Nonlinear Time-Varying Systems

arXiv: https://arxiv.org/abs/2210.06272 · HTML: https://mlsanity.com/paper/2210.06272/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2022.

## Built on by (most cited first, 11 of 11)

- [Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om method](https://mlsanity.com/paper/2403.02811/) (2024)
- [Optimal Control of Nonlinear Systems with Unknown Dynamics](https://mlsanity.com/paper/2305.15188/) (2023)
- [Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD](https://mlsanity.com/paper/2408.06607/) (2024)
- [Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data](https://mlsanity.com/paper/2505.04954/) (2025)
- [MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems](https://mlsanity.com/paper/2510.09042/) (2025)
- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)
- [Conformal Online Learning of Deep Koopman Linear Embeddings](https://mlsanity.com/paper/2511.12760/) (2025)
- [Efficient Reinforcement Learning using Linear Koopman Dynamics for Nonlinear Robotic Systems](https://mlsanity.com/paper/2604.19980/) (2026)
- [Bilinear Mamba-Koopman Neural MPC for Varying Dynamics](https://mlsanity.com/paper/2605.04793/) (2026)
- [MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts](https://mlsanity.com/paper/2607.26345/) (2026)
- [Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis](https://mlsanity.com/paper/2609.04329/) (2026)

## Abstract (arXiv)

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which is resulted from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.