[IMS Seminar] Inferring the Unknown Parameters in Differential Equation by Gaussian Process Regression with Constraint

ON2022-06-15TAG: ShanghaiTech UniversityCATEGORY: Lecture

Time:Friday, June 17th, 2022, 09:00-10:00

Location:Tecent Meeting

Link:  https://meeting.tencent.com/dm/a75Qu1bLhAcw 

Room Number: 460-868-847

Speaker:  Hongqiao Wang,  Central South University

Abstract: In this work, we propose a Bayesian inference framework to solve the problem of estimating the parameters of the DE model, from the given noisy and scarce observations of the solution only.A key issue in this problem is to robustly estimate the derivatives of the solution function from noisy observations of only the function values at given location points, under the assumption of a physical model in the form of differential equation governing the function and its derivatives. To address the key issue, we propose to use the Gaussian Process Regression with Constraint (GPRC) method which jointly model the solution, its derivatives, and the parametric differential equation, to estimate thesolution and its derivatives. For nonlinear differential equations, a Picard-iteration-like approximation of linearization method is used so that the GPRC can be still iteratively applicable. A new and reasonable potential which combines the data and equation information, is proposed and used in the likelihood for our inference. With numerical examples, we illustrate that the proposed method has competitive performance against existing approaches for estimating the unknown parameters in DEs.