The Stochastic Occupation Kernel Method for System Identification

2024/06/21 by Michael Wells, Wells, Michael, Kamel Lahouel +3
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2406.15661

openalex publication_date 2024/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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