text: abstract
  we consider the problem of approximating the output of a parametric electromagnetic field
  model in the presence of a large number of uncertain input parameters. given a sufficiently
  smooth output with respect to the input parameters, such problems are often tackled with
  interpolation-based approaches, such as the stochastic collocation method on tensor-product or
  isotropic sparse grids. due to the so-called curse of dimensionality, those approaches result in
  increased or even forbidding computational costs. in order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive, hierarchical interpolation
  scheme, based on nested univariate interpolation nodes. clenshaw-curtis and leja nodes satisfy the nestedness property and have been found to provide accurate interpolations when the
  parameters follow uniform distributions. the dimension-adaptive algorithm constructs the approximation based on the observation that not all parameters or interactions among them are
  equally important regarding their impact on the model’s output. our goal is to exploit this
  anisotropy in order to construct accurate polynomial surrogate models at a reduced computational cost compared to isotropic sparse grids. we apply the stochastic collocation method
  to two electromagnetic field models with medium- to high-dimensional input uncertainty. the
  performances of isotropic and adaptively constructed, anisotropic sparse grids based on both
  clenshaw-curtis and leja interpolation nodes are examined. all considered approaches are
  compared with one another regarding the surrogate models’ approximation accuracies using a
  cross-validation error metric.
  keywords– dimension adaptivity, clenshaw-curtis, computational electromagnetics, electromagnetic field simulations, hierarchical interpolation, leja, sparse grids, stochastic collocation,
  uncertainty quantification.