Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	王文佳，香港科技大学（广州）
Inviter:	熊世峰
Title:	Functional-Input Gaussian Processes
Language:	Chinese
Time & Venue:	2022.12.26 15:00-16:00 腾讯会议:992-443-132
Abstract:	Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are scarce. Motivated by an inverse scattering problem in which functional inputs representing the support and material properties of the scatterer are involved in the partial differential equations, a new class of kernel functions for functional inputs is introduced for GPs. Based on the proposed GP models, the asymptotic convergence properties of the resulting mean squared prediction errors are derived and the finite sample performance is demonstrated by numerical examples. In the application to inverse scattering, a surrogate model is constructed with functional inputs, which is crucial to recover the reflective index of an inhomogeneous isotropic scattering region of interest for a given far-field pattern.