Seminar for machine learning and UQ in scientific computing Laura Scarabosio

Laura Scarabosio (Radboud University): Deep neural network surrogates for transmission problems with geometric uncertainties

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Laura Scarabosio (Radboud University): Deep neural network surrogates for transmission problems with geometric uncertainties

We consider the point evaluation of the solution to interface problems with geometric uncertainties, where the uncertainty in the obstacle is described by a high-dimensional parameter, as a prototypical example of non-smooth dependence of a quantity of interest on the parameter. We focus in particular on an elliptic interface problem and a Helmholtz transmission problem. The non-smooth parameter dependence poses a challenge when one is interested in building surrogates. In this talk we propose to use deep neural networks for this purpose. We provide a theoretical justification for why we expect neural networks to provide good surrogates. Furthermore, we present numerical experiments showing their good performance in practice. We observe in particular that neural networks do not suffer from the curse of dimensionality, and we study the dependence of the error on the number of point evaluations (which coincides with the number of discontinuities in the parameter space), as well as on several modeling parameters, such as the contrast between the two materials and, for the Helmholtz transmission problem, the wavenumber.