Abstract

 In this talk, we discuss three kinds of random Helmholtz problems. For the random interface grating problems, by using the asymptotic perturbation approach via shape derivative, we estimate the expectation and the variance of the random solution in terms of the magnitude of the perturbation. For the optimal control problems constrained by random Helmholtz equation, we preprocess certain quantities before the ADMM iteration, so that nearly no random variable is in the inner iteration. For the inverse scattering problem, we propose a machine learning method for the data retrieval, which can effectively cope with the reconstruction under limited-aperture and/or phaseless far-field data. Numerical experiments verify the promising features of our schemes.