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In this thesis, global surrogate models for responses of expensive simulations are investigated. Computational fluid dynamics (CFD) have become an indispensable tool in the aircraft industry. But simulations of realistic aircraft configurations remain challenging and computationally expensive despite the sustained advances in computing power. With the demand for numerous simulations to describe the behavior of an output quantity over a design space, the need for surrogate models arises. They are easy to evaluate and approximate quantities of interest of a computer code. Only a few number of evaluations of the simulation are stored for determining the behavior of the response over a whole range of the input parameter domain. The Kriging method is capable of interpolating highly nonlinear, deterministic functions based on scattered datasets. Using correlation functions, distinct sensitivities of the response with respect to the input parameters can be considered automatically. Kriging can be extended to incorporate not only evaluations of the simulation, but also gradient information, which is called gradient-enhanced Kriging. Adaptive sampling strategies can generate more efficient surrogate models. Contrary to traditional one-stage approaches, the surrogate model is built step-by-step. In every stage of an adaptive process, the current surrogate is assessed in order to determine new sample locations, where the response is evaluated and the new samples are added to the existing set of samples. In this way, the sampling strategy learns about the behavior of the response and a problem-specific design is generated. Critical regions of the input parameter space are identified automatically and sampled more densely for reproducing the response's behavior correctly. The number of required expensive simulations is decreased considerably. All these approaches treat the response itself more or less as an unknown output of a black-box. A new approach is motivated by the assumption that for a predefined problem class, the behavior of the response is not arbitrary, but rather related to other instances of the mutual problem class. In CFD, for example, responses of aerodynamic coefficients share structural similarities for different airfoil geometries. The goal is to identify the similarities in a database of responses via principal component analysis and to use them for a generic surrogate model. Characteristic structures of the problem class can be used for increasing the approximation quality in new test cases. Traditional approaches still require a large number of response evaluations, in order to achieve a globally high approximation quality. Validating the generic surrogate model for industrial relevant test cases shows that they generate efficient surrogates, which are more accurate than common interpolations. Thus practical, i.e. affordable surrogates are possible already for moderate sample sizes. So far, interpolation problems were regarded as separate problems. The new approach uses the structural similarities of a mutual problem class innovatively for surrogate modeling. Concepts from response surface methods, variable-fidelity modeling, design of experiments, image registration and statistical shape analysis are connected in an interdisciplinary way. Generic surrogate modeling is not restricted to aerodynamic simulation. It can be applied, whenever expensive simulations can be assigned to a larger problem class, in which structural similarities are expected.
In order to discuss potential sustainability issues of expanding silage maize cultivation in Rhineland-Palatinate, spatially explicit monitoring is necessary. Publicly available statistical records are often not a sufficient basis for extensive research, especially on soil health, where risk factors like erosion and compaction depend on variables that are specific to every site, and hard to generalize for larger administrative aggregates. The focus of this study is to apply established classification algorithms to estimate maize abundance for each independent pixel, while at the same time accounting for their spatial relationship. Therefore, two ways to incorporate spatial autocorrelation of neighboring pixels are combined with three different classification models. The performance of each of these modeling approaches is analyzed and discussed. Finally, one prediction approach is applied to the imagery, and the overall predicted acreage is compared to publicly available data. We were able to show that Support Vector Machine (SVM) classification and Random Forests (RF) were able to distinguish maize pixels reliably, with kappa values well above 0.9 in most cases. The Generalized Linear Model (GLM) performed substantially worse. Furthermore, Regression Kriging (RK) as an approach to integrate spatial autocorrelation into the prediction model is not suitable in use cases with millions of sparsely clustered training pixels. Gaussian Blur is able to improve predictions slightly in these cases, but it is possible that this is only because it smoothes out impurities of the reference data. The overall prediction with RF classification combined with Gaussian Blur performed well, with out of bag error rates of 0.5% in 2009 and 1.3% in 2016. Despite the low error rates, there is a discrepancy between the predicted acreage and the official records, which is 20% in 2009 and 27% in 2016.