Enhanced adaptive surrogate models with applications in uncertainty quantification for nanoplasmonics

TL;DR

This paper introduces an improved surrogate modeling approach for uncertainty quantification in nanoplasmonics, combining conformal maps and adjoint error correction with a dimension-adaptive collocation scheme, enabling efficient analysis of complex optical systems.

Contribution

It advances surrogate modeling by integrating conformal maps and adjoint error correction into a dimension-adaptive collocation framework for nanoplasmonics applications.

Findings

Enhanced surrogate models improve uncertainty quantification accuracy.

The method effectively handles multiple random parameters.

Numerical studies demonstrate the approach's benefits and limitations.

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.