# The occupation kernel method

October 15, 2024 — October 15, 2024

calculus

dynamical systems

functional analysis

Gaussian

generative

geometry

Hilbert space

how do science

kernel tricks

machine learning

PDEs

physics

regression

sciml

SDEs

signal processing

statistics

statmech

stochastic processes

time series

uncertainty

Kernel tricks for trajectories. That is to say, the other kernel trick for trajectories.

I am told e.g. that this generalises the Radon transform, as seen in tomography, so I guess I should know about that for my own work.

Applications include the identification of forcing fields for functions by sparsely observable trajectories, without finite-difference approximations, for system identification and functional inverse problems.

## 1 References

Li, and Rosenfeld. 2021. “Fractional Order System Identification with Occupation Kernel Regression.” In

*2021 American Control Conference (ACC)*.
Rosenfeld, Kamalapurkar, Russo, et al. 2019. “Occupation Kernels and Densely Defined Liouville Operators for System Identification.” In

*2019 IEEE 58th Conference on Decision and Control (CDC)*.
Rosenfeld, Russo, Kamalapurkar, et al. 2024. “The Occupation Kernel Method for Nonlinear System Identification.”

*SIAM Journal on Control and Optimization*.
Russo, Kamalapurkar, Chang, et al. 2021. “Motion Tomography via Occupation Kernels.”

Wells, Lahouel, and Jedynak. 2024. “The Stochastic Occupation Kernel Method for System Identification.”