TY - JOUR A1 - Plock, Matthias A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel A1 - Schütte, Christof T1 - Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions JF - Metrologia N2 - In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results. Y1 - 2023 U6 - https://doi.org/10.1088/1681-7575/ace4cd VL - 60 SP - 054001 ER - TY - JOUR A1 - Plock, Matthias A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology JF - Proc. SPIE Y1 - 2021 U6 - https://doi.org/10.1117/12.2592266 VL - 11783 SP - 117830J ER - TY - JOUR A1 - Semler, Phillip A1 - Weiser, Martin T1 - Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems JF - Inverse Problems N2 - In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model y with a surrogate model y(s) that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that y(s) is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures. Y1 - 2023 U6 - https://doi.org/10.1088/1361-6420/ad0028 VL - 39 IS - 12 SP - 125003 ER - TY - JOUR A1 - Rickert, Lucas A1 - Betz, Fridtjof A1 - Plock, Matthias A1 - Burger, Sven A1 - Heindel, Tobias T1 - High-performance designs for fiber-pigtailed quantum-light sources based on quantum dots in electrically-controlled circular Bragg gratings JF - Opt. Express Y1 - 2023 U6 - https://doi.org/10.1364/OE.486060 VL - 31 SP - 14750 ER - TY - JOUR A1 - Bopp, Julian M. A1 - Plock, Matthias A1 - Turan, Tim A1 - Pieplow, Gregor A1 - Burger, Sven A1 - Schröder, Tim T1 - Sawfish Photonic Crystal Cavity for Near-Unity Emitter-to-Fiber Interfacing in Quantum Network Applications JF - Adv. Opt. Mater. Y1 - 2024 U6 - https://doi.org/10.1002/adom.202301286 VL - 12 SP - 2301286 ER - TY - JOUR A1 - Plock, Matthias A1 - Binkowski, Felix A1 - Zschiedrich, Lin A1 - Schneider, Phillip-Immanuel A1 - Burger, Sven T1 - Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes JF - J. Opt. Soc. Am. B Y1 - 2024 U6 - https://doi.org/10.1364/JOSAB.505767 VL - 41 SP - 850 ER - TY - JOUR A1 - Plock, Matthias A1 - Andrle, Kas A1 - Burger, Sven A1 - Schneider, Philipp-Immanuel T1 - Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction JF - Adv. Theory Simul. Y1 - 2022 U6 - https://doi.org/10.1002/adts.202200112 VL - 5 SP - 2200112 ER -