44 research outputs found
Robust Adaptive Least Squares Polynomial Chaos Expansions in High-Frequency Applications
We present an algorithm for computing sparse, least squares-based polynomial
chaos expansions, incorporating both adaptive polynomial bases and sequential
experimental designs. The algorithm is employed to approximate stochastic
high-frequency electromagnetic models in a black-box way, in particular, given
only a dataset of random parameter realizations and the corresponding
observations regarding a quantity of interest, typically a scattering
parameter. The construction of the polynomial basis is based on a greedy,
adaptive, sensitivity-related method. The sequential expansion of the
experimental design employs different optimality criteria, with respect to the
algebraic form of the least squares problem. We investigate how different
conditions affect the robustness of the derived surrogate models, that is, how
much the approximation accuracy varies given different experimental designs. It
is found that relatively optimistic criteria perform on average better than
stricter ones, yielding superior approximation accuracies for equal dataset
sizes. However, the results of strict criteria are significantly more robust,
as reduced variations regarding the approximation accuracy are obtained, over a
range of experimental designs. Two criteria are proposed for a good
accuracy-robustness trade-off.Comment: 17 pages, 7 figures, 2 table
An hpâadaptive multiâelement stochastic collocation method for surrogate modeling with information reâuse
This article introduces an hpâadaptive multiâelement stochastic collocation method, which additionally allows to reâuse existing model evaluations during either hâ or pârefinement. The collocation method is based on weighted Leja nodes. After hârefinement, local interpolations are stabilized by adding and sorting Leja nodes on each newly created subâelement in a hierarchical manner. For pârefinement, the local polynomial approximations are based on totalâdegree or dimensionâadaptive bases. The method is applied in the context of forward and inverse uncertainty quantification to handle nonâsmooth or strongly localized response surfaces. The performance of the proposed method is assessed in several test cases, also in comparison to competing methods
Quadrupole Magnet Design based on Genetic Multi-Objective Optimization
This work suggests to optimize the geometry of a quadrupole magnet by means
of a genetic algorithm adapted to solve multi-objective optimization problems.
To that end, a non-domination sorting genetic algorithm known as NSGA-III is
used. The optimization objectives are chosen such that a high magnetic field
quality in the aperture of the magnet is guaranteed, while simultaneously the
magnet design remains cost-efficient. The field quality is computed using a
magnetostatic finite element model of the quadrupole, the results of which are
post-processed and integrated into the optimization algorithm. An extensive
analysis of the optimization results is performed, including Pareto front
movements and identification of best designs.Comment: 22 pages, 7 figure
Optimization and uncertainty quantification of gradient index metasurfaces
The design of intrinsically flat two-dimensional optical components, i.e., metasurfaces,
generally requires an extensive parameter search to target the appropriate scattering properties
of their constituting building blocks. Such design methodologies neglect important near-field
interaction effects, playing an essential role in limiting the device performance. Optimization
of transmission, phase-addressing and broadband performances of metasurfaces require new
numerical tools. Additionally, uncertainties and systematic fabrication errors should be analysed.
These estimations, of critical importance in the case of large production of metaoptics components,
are useful to further project their deployment in industrial applications. Here, we report on a
computational methodology to optimize metasurface designs. We complement this computational
methodology by quantifying the impact of fabrication uncertainties on the experimentally
characterized components. This analysis provides general perspectives on the overall metaoptics
performances, giving an idea of the expected average behavior of a large number of devices
Adaptive approximations for high-dimensional uncertainty quantification in stochastic parametric electromagnetic field simulations
The present work addresses the problems of high-dimensional approximation and uncertainty quantification in the context of electromagnetic field simulations. In the presence of many parameters, one faces the so-called curse of dimensionality. The focus of this work lies on adaptive methods that mitigate the effect of the curse of dimensionality, and therefore enable otherwise intractable uncertainty quantification studies. Its application scope includes electromagnetic field models suffering from moderately high-dimensional input uncertainty. However, the presented methods can be used in a black-box fashion and are therefore applicable to other types of problems as well
Adaptive approximations for high-dimensional uncertainty quantification in stochastic parametric electromagnetic field simulations
The present work addresses the problems of high-dimensional approximation and uncertainty quantification in the context of electromagnetic field simulations. In the presence of many parameters, one faces the so-called curse of dimensionality. The focus of this work lies on adaptive methods that mitigate the effect of the curse of dimensionality, and therefore enable otherwise intractable uncertainty quantification studies. Its application scope includes electromagnetic field models suffering from moderately high-dimensional input uncertainty. However, the presented methods can be used in a black-box fashion and are therefore applicable to other types of problems as well
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
status: publishe