# Kalman Filter Aided Federated Koopman Learning

arXiv: https://arxiv.org/abs/2507.04808 · HTML: https://mlsanity.com/paper/2507.04808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Asynchronous Federated Learning on Heterogeneous Devices: A Survey](https://mlsanity.com/paper/2109.04269/) (2021)
- [Federated Learning Enables Big Data for Rare Cancer Boundary Detection](https://mlsanity.com/paper/2204.10836/) (2022)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Integrated Sensing and Communication Signals Toward 5G-A and 6G: A Survey](https://mlsanity.com/paper/2301.03857/) (2023)
- [Learning from Data with Heterogeneous Noise using SGD](https://mlsanity.com/paper/1412.5617/) (2014)
- [A Unified Filter Method for Jointly Estimating State and Parameters of Stochastic Dynamical Systems via the Ensemble Score Filter](https://mlsanity.com/paper/2312.10503/) (2023)
- [Linearization of Time-Varying Nonlinear Systems Using A Modified Linear Iterative Method](https://mlsanity.com/paper/1404.5901/) (2014)

## Built on by (most cited first, 1 of 1)

- [Federated Nonlinear System Identification](https://mlsanity.com/paper/2508.15025/) (2025)

## Abstract (arXiv)

Real-time control and estimation are pivotal for applications such as industrial automation and future healthcare. The realization of this vision relies heavily on efficient interactions with nonlinear systems. Therefore, Koopman learning, which leverages the power of deep learning to linearize nonlinear systems, has been one of the most successful examples of mitigating the complexity inherent in nonlinearity. However, the existing literature assumes access to accurate system states and abundant high-quality data for Koopman analysis, which is usually impractical in real-world scenarios. To fill this void, this paper considers the case where only observations of the system are available and where the observation data is insufficient to accomplish an independent Koopman analysis. To this end, we propose Kalman Filter aided Federated Koopman Learning (KF-FedKL), which pioneers the combination of Kalman filtering and federated learning with Koopman analysis. By doing so, we can achieve collaborative linearization with privacy guarantees. Specifically, we employ a straightforward yet efficient loss function to drive the training of a deep Koopman network for linearization. To obtain system information devoid of individual information from observation data, we leverage the unscented Kalman filter and the unscented Rauch-Tung-Striebel smoother. To achieve collaboration between clients, we adopt the federated learning framework and develop a modified FedAvg algorithm to orchestrate the collaboration. A convergence analysis of the proposed framework is also presented. Finally, through extensive numerical simulations, we showcase the performance of KF-FedKL under various situations.