# The Stochastic Occupation Kernel Method for System Identification

arXiv: https://arxiv.org/abs/2406.15661 · HTML: https://mlsanity.com/paper/2406.15661/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 8 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 4 of 4)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [The Occupation Kernel Method for Nonlinear System Identification](https://mlsanity.com/paper/1909.11792/) (2019)

## Built on by (most cited first, 1 of 1)

- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)

## Abstract (arXiv)

The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations.