Enhanced adaptive surrogate models with applications in uncertainty quantification for nanoplasmonics

Abstract

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal maps and adjoint error correction. The methodology is applied to Maxwell's source problem with random input data. This setting comprises many applications of current interest from computational nanoplasmonics, such as grating couplers or optical waveguides. Using a non-trivial benchmark model we show the benefits and drawbacks of using enhanced surrogate models through various numerical studies. The proposed strategy allows us to conduct a thorough uncertainty analysis, taking into account a moderately large number of random parameters.