(untitled) (Communications in Mathematical Research, 2021)
Consider an inverse problem that aims to identify key statistical properties of the profile for the unknown random perfectly conducting grating structure by boundary measurements of the diffracted fields in transverse magnetic polarization. The method proposed in this paper is based on a novel combination of the Monte Carlo technique, a continuation method and the Karhunen-Loève expansion for the uncertainty quantification of the random structure. Numerical results are presented to demonstrate the effectiveness of the proposed method.