The Stochastic Occupation Kernel Method for System Identification

TL;DR

This paper introduces a novel two-step non-parametric method using occupation kernels to identify both drift and diffusion components of stochastic differential equations from data snapshots, enhancing system modeling accuracy.

Contribution

It presents a new approach combining occupation kernels and semi-definite programming to learn stochastic differential equations without assuming parametric forms.

Findings

Successfully learned drift and diffusion from simulated data

Demonstrated effectiveness on example stochastic systems

Provided a framework for non-parametric system identification

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.