--- title: The occupation kernel method date: '2024-10-15T17:35:39+11:00' date-modified: '2024-10-15T17:35:47+11:00' link-citations: true bibupdated: '2024-10-15T17:45:39' slug: kernel_occupation nocite: - '@*' bibliography: kernel_occupation.yaml bibliography-alt: kernel_occupation.bib csl: minimalist.csl reference-section-title: References image: ../images/de_paus_RP-P-OB-78.844.thumbnail.avif categories: - 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 polish: 0 novelty: 0 certainty: 1 usefulness: 0 --- The occupation kernel method — The Dan MacKinlay stable of variably-well-consider’d enterprises

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
Figure 1

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 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.”