We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of dimensions, we employ a dimensionadaptive stochastic collocation method based on nested univariate nodes. We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the cases of uniform and bounded, non-uniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate case and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented.keywordsdimension adaptivity, Clenshaw-Curtis, computational electromagnetics, Leja, sparse grids, stochastic collocation, uncertainty quantification.

This work presents a data-driven magnetostatic finite-element solver that is specifically well suited to cope with strongly nonlinear material responses. The data-driven computing framework is essentially a multiobjective optimization procedure matching the material operation points as closely as possible to given material data while obeying Maxwell's equations. Here, the framework is extended with heterogeneous (local) weighting factors-one per finite element-equilibrating the goal function locally according to the material behavior. This modification allows the data-driven solver to cope with unbalanced measurement data sets, that is, data sets suffering from unbalanced space filling. This occurs particularly in the case of strongly nonlinear materials, which constitute problematic cases that hinder the efficiency and accuracy of standard data-driven solvers with a homogeneous (global) weighting factor. The local weighting factors are embedded in the distance-minimizing data-driven algorithm used for noiseless data, likewise for the maximum entropy data-driven algorithm used for noisy data. Numerical experiments based on a quadrupole magnet model with a soft magnetic material show that the proposed modification results in major improvements in terms of solution accuracy and solver efficiency. For the case of noiseless data, local weighting factors improve the convergence of the data-driven solver by orders of magnitude. When noisy data are considered, the convergence rate of the data-driven solver is doubled.

This paper develops a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points are minimized while enforcing Maxwell's equations. The minimization problem is solved by employing the Lagrange multiplier approach. The procedure wraps the FE method within an outer data-driven iteration. The method is capable of considering anisotropic materials and is adapted to deal with models featuring a combination of exact material knowledge and measured material data. Thereto, three approaches with an increasing level of intrusivity according to the FE formulation are proposed. The numerical results for a quadrupole-magnet model show that data-driven field simulation is feasible and affordable and overcomes the need of modeling the material law.

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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.

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.keywordspolynomial chaos, surrogate modeling, high-frequency electromagnetic devices, least squares regression, adaptive basis, sequential experimental design

Recent experiments have shown that spatial dispersion may have a conspicuous impact on the response of plasmonic structures. This suggests that in some cases the Drude model should be replaced by more advanced descriptions that take spatial dispersion into account, like the hydrodynamic model. Here we show that nonlocality in the metallic response affects surface plasmons propagating at the interface between a metal and a dielectric with high permittivity. As a direct consequence, any nanoparticle with a radius larger than 20 nm can be expected to be sensitive to spatial dispersion whatever its size. The same behavior is expected for a simple metallic grating allowing the excitation of surface plasmons, just as in Woods famous experiment. Finally, we carefully set up a procedure to measure the signature of spatial dispersion precisely, leading the way for future experiments. Importantly, our work suggests that for any plasmonic structure in a high permittivity dielectric, nonlocality should be taken into account.

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction of the computational time is observed as well.