# The Occupation Kernel Method for Nonlinear System Identification

arXiv: https://arxiv.org/abs/1909.11792 · HTML: https://mlsanity.com/paper/1909.11792/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

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

- [Convergence of weak-SINDy Surrogate Models](https://mlsanity.com/paper/2209.15573/) (2022)
- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [MOCK: an Algorithm for Learning Nonparametric Differential Equations via Multivariate Occupation Kernel Functions](https://mlsanity.com/paper/2306.10189/) (2023)
- [The Stochastic Occupation Kernel Method for System Identification](https://mlsanity.com/paper/2406.15661/) (2024)
- [Occupation Kernel Hilbert Spaces for Fractional Order Liouville Operators and Dynamic Mode Decomposition](https://mlsanity.com/paper/2102.13266/) (2021)
- [Control Occupation Kernel Regression for Nonlinear Control-Affine Systems](https://mlsanity.com/paper/2106.00103/) (2021)
- [Singular Dynamic Mode Decompositions](https://mlsanity.com/paper/2106.02639/) (2021)
- [Fault Detection via Occupation Kernel Principal Component Analysis](https://mlsanity.com/paper/2303.11138/) (2023)
- [Exact identification of nonlinear dynamical systems by Trimmed Lasso](https://mlsanity.com/paper/2308.01891/) (2023)
- [An appointment with Reproducing Kernel Hilbert Space generated by Generalized Gaussian RBF as L2-measure](https://mlsanity.com/paper/2312.10693/) (2023)
- [The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations](https://mlsanity.com/paper/2505.11622/) (2025)

## Abstract (arXiv)

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions, and establishes Liouville operators over RKHS where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately, while also exhibiting a certain robustness to noise.