[NA] Fernando José Henriquez Barraza: Shape Uncertainty Quantification in Acoustic and Electromagnetic Scattering

17 February 2023 12:30 till 13:30 - Location: van der Poelzaal (EWI, LB 01.220) | Add to my calendar

In this talk, we consider the propagation of acoustic and electromagnetic waves in domains of uncertain shape. We are particularly interested in quantifying the effect on these perturbations on the involved fields and possibly into other quantities of interest. After considering a domain or surface parametrization with countably-many parameters, one obtains a high-dimensional parametric map describing the problem's solution manifold. The design and analysis of a variety of methods commonly used in computational uncertainty quantification (UQ for short) affording provably dimension-independent convergence rates rely on the holomorphic dependence of the problem's solution upon the parametric input. When the parametric input encodes a family of domain or boundary transformations, the holomorphic dependence of the problem upon the parametric input is usually referred to as shape holomorphy. We present and discuss the key technicalities involved in the verification of this property for different models including: volume formulation of the Helmholtz problem, boundary integral formulation, volume integral equations, boundary integral formulations for multiple disjoint arcs, among others. We discuss the importance of this property in the implementation and analysis of different techniques used in forward and inverse computational shape UQ for the previously described models and the implications in the constructions efficient surrogates using neural networks.