Summary of The Stochastic Occupation Kernel Method For System Identification, by Michael Wells et al.
The Stochastic Occupation Kernel Method for System Identification
by Michael Wells, Kamel Lahouel, Bruno Jedynak
First submitted to arxiv on: 21 Jun 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Systems and Control (eess.SY)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed method uses occupation kernels to learn ordinary differential equations from data in a non-parametric manner. A two-step approach is taken to learn the drift and diffusion of stochastic differential equations given process snapshots. The drift is first learned by applying the occupation kernel algorithm to the expected value of the process, followed by learning the diffusion using a semi-definite program. The method learns the diffusion squared as a non-negative function in a reproducing kernel Hilbert space associated with the square of a kernel. Simulations and examples are presented. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A group of scientists developed a new way to understand ordinary differential equations (ODEs) that come from data. They used a technique called occupation kernels, which is good at learning things without assuming what they should look like. The team came up with a two-step plan: first, they figured out the “drift” part of the ODE, and then they used that to learn the “diffusion” part. This was done by solving a special kind of math problem. They showed how their method works using examples and computer simulations. |
Keywords
* Artificial intelligence * Diffusion
