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Benefits and application of tree structures in Gaussian process models to optimize magnetic field shaping problems. (English) Zbl 1397.62616
Pilz, Jürgen (ed.) et al., Statistics and simulation. Contributions given at the 8th international workshop on simulation, IWS 8, Vienna, Austria, September 21–25, 2015. Cham: Springer (ISBN 978-3-319-76034-6/hbk; 978-3-319-76035-3/ebook). Springer Proceedings in Mathematics & Statistics 231, 161-170 (2018).
Summary: Recent years have witnessed the development of powerful numerical methods to emulate realistic physical systems and their integration into the industrial product development process. Today, finite element simulations have become a standard tool to help with the design of technical products. However, when it comes to multivariate optimization, the computation power requirements of such tools can often not be met when working with classical algorithms. As a result, a lot of attention is currently given to the design of computer experiments approach. One goal of this work is the development of a sophisticated optimization process for simulation based models. Within many possible choices, Gaussian process models are most widely used as modeling approach for the simulation data. However, these models are strongly based on stationary assumptions that are often not satisfied in the underlying system. In this work, treed Gaussian process models are investigated for dealing with non-stationarities and compared to the usual modeling approach. The method is developed for and applied to the specific physical problem of the optimization of 1D magnetic linear position detection.
For the entire collection see [Zbl 1398.62008].

62P35 Applications of statistics to physics
60G15 Gaussian processes
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