# Federated Nonlinear System Identification

arXiv: https://arxiv.org/abs/2508.15025 · HTML: https://mlsanity.com/paper/2508.15025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator](https://mlsanity.com/paper/2003.07937/) (2020)
- [FedSysID: A Federated Approach to Sample-Efficient System Identification](https://mlsanity.com/paper/2211.14393/) (2022)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees](https://mlsanity.com/paper/2411.00656/) (2024)
- [Irrelevance of linear controllability to nonlinear dynamical networks](https://mlsanity.com/paper/1909.01288/) (2019)
- [Kalman Filter Aided Federated Koopman Learning](https://mlsanity.com/paper/2507.04808/) (2025)

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

- [Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization](https://mlsanity.com/paper/2511.17489/) (2025)

## Abstract (arXiv)

We consider federated learning of linearly-parameterized nonlinear systems. We establish theoretical guarantees on the effectiveness of federated nonlinear system identification compared to centralized approaches, demonstrating that the convergence rate improves as the number of clients increases. Although the convergence rates in the linear and nonlinear cases differ only by a constant, this constant depends on the feature map φ, which can be carefully chosen in the nonlinear setting to increase excitation and improve performance. We experimentally validate our theory in physical settings where client devices are driven by i.i.d. control inputs and control policies exhibiting i.i.d. random perturbations, ensuring non-active exploration. Experiments use trajectories from nonlinear dynamical systems characterized by real-analytic feature functions, including polynomial and trigonometric components, representative of physical systems including pendulum and quadrotor dynamics. We analyze the convergence behavior of the proposed method under varying noise levels and data distributions. Results show that federated learning consistently improves convergence of any individual client as the number of participating clients increases.