In computational electromagnetics, simulations often need to be evaluated repeatedly for different parameters. Performing full numerical simulations for each parameter configuration can be computationally expensive.

Recent works have explored the use of machine learning techniques, such as deep neural networks (DNNs), Gaussian processes (GPs) and Polynomial Chaos Expansion (PCE), to learn parametric solutions of electromagnetic problems. These approaches enable fast predictions once a model has been trained. In particular they learn the solution in terms of coefficients with respect to a (possibly reduced) finite element or isogeometric basis.

In this thesis, regression-based PCE will be explored as an alternative approach for gradient-enhanced learning. This framework represents the parametric dependence of the solution in terms of a series expansion in orthogonal polynomials.

The thesis will involve a literature review on PCE and the implementation of a PCE-based surrogate model for parametric electromagnetic problems. If time permits, residual-based error estimators or predictive uncertainty intervals for the surrogate model can also be explored.