The occupation kernel method

October 15, 2024 — October 15, 2024

Suspiciously similar content

Kernel tricks for trajectories. That is to say, another 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 Incoming

The Incredible Occupation Kernel! // A peek at my research (video)
The Learning Dock Group

We capture governing principles of dynamical systems with operators.

There is a host of natural phenomena that is impossible to describe from first principles. We design algorithms that use captured snapshots of occurrences, and we use concepts from operator and Hilbert space theory to uncover the underlying governing principles of our world.
Reproducing Kernels and Functionals (Theory of Machine Learning) (video)

2 References

Li, and Rosenfeld. 2021. “Fractional Order System Identification with Occupation Kernel Regression.” In 2021 American Control Conference (ACC).

Rielly, Lahouel, Lew, et al. 2025. “MOCK: An Algorithm for Learning Nonparametric Differential Equations via Multivariate Occupation Kernel Functions.”

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.”