KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging

Several strategies relying on kriging have recently been proposed for adaptively estimating contour lines and excursion sets of functions under severely limited evaluation budget. The recently released R package KrigInv 3 is presented and offers a sound implementation of various sampling criteria for those kinds of inverse problems. KrigInv is based on the DiceKriging package, and thus benefits from a number of options concerning the underlying kriging models. Six implemented sampling criteria are detailed in a tutorial and illustrated with graphical examples. Different functionalities of KrigInv are gradually explained. Additionally, two recently proposed criteria for batch-sequential inversion are presented, enabling advanced users to distribute function evaluations in parallel on clusters or clouds of machines. Finally, auxiliary problems are discussed. These include the fine tuning of numerical integration and optimization procedures used within the computation and the optimization of the considered criteria.

Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package

Kriging-based optimization relying on noisy evaluations of complex systems has recently motivated contributions from various research communities. Five strategies have been implemented in the DiceOptim package. The corresponding functions constitute a user-friendly tool for solving expensive noisy optimization problems in a sequential framework, while offering some flexibility for advanced users. Besides, the implementation is done in a unified environment, making this package a useful device for studying the relative performances of existing approaches depending on the experimental setup. An overview of the package structure and interface is provided, as well as a description of the strategies and some insight about the implementation challenges and the proposed solutions. The strategies are compared to some existing optimization packages on analytical test functions and show promising performances.

Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Hypercoagulation and hyperkinetic blood pressure indicative of physiological loss-of-control despite behavioural control in Africans: The SABPA study.

OBJECTIVES A dissociation between behavioural (in-control) and physiological parameters (indicating loss-of-control) is associated with cardiovascular risk in defensive coping (DefS) Africans. We evaluated relationships between DefS, sub-clinical atherosclerosis, low-grade inflammation and hypercoagulation in a bi-ethnic sex cohort. METHODS Black (Africans) and white Africans (Caucasians) (n = 375; aged 44.6 ± 9.7 years) were included. Ambulatory BP, vascular structure (left carotid cross-sectional wall area (L-CSWA) and plaque counts), and markers of coagulation and inflammation were quantified. Ethnicity/coping style interaction was revealed only in DefS participants. RESULTS A hypertensive state, less plaque, low-grade inflammation, and hypercoagulation were more prevalent in DefS Africans (27-84%) than DefS Caucasians (18-41%). Regression analyses demonstrated associations between L-CSWA and 24 hour systolic BP (R(2) = 0.38; β = 0.78; p < 0.05) in DefS African men but not in DefS African women or Caucasians. No associations between L-CSWA and coagulation markers were evident. CONCLUSION Novel findings revealed hypercoagulation, low-grade inflammation and hyperkinetic BP (physiological loss-of-control responses) in DefS African men. Coupled to a self-reported in-control DefS behavioural profile, this reflects dissociation between behaviour and physiology. It may explain changes in vascular structure, increasing cerebrovascular disease risk in a state of hyper-vigilant coping.

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Contents and stable carbon isotope compositions of biomarkers indicative for AOM-communities dominated by different ANME groups in two carbonate samples from Hydrate Hole pockmark

Different types of seep carbonates were recovered from the 'Kouilou pockmarks' on the Congo deep-sea fan in approximately 3100 m water depth. The carbonate aggregates are represented by pyritiferous nodules, crusts and slabs, tubes, and filled molds. The latter are interpreted to represent casts of former burrows of bivalves and holothurians. The nodules consisting of high-Mg-calcite apparently formed deeper within the sediments than the predominantly aragonitic crusts and slabs. Nodule formation was caused by anaerobic oxidation of methane dominantly involving archaea of the phylogenetic ANME-1 group, whereas aragonitic crusts resulted from the activity of archaea of the ANME-2 cluster. Evidence for this correlation is based on the distribution of specific biomarkers in the two types of carbonate aggregates, showing higher hydroxyarchaeol to archaeol ratios in the crusts as opposed to nodules. Formation of crusts closer to the seafloor than nodules is indicated by higher carbonate contents of crusts, probably reflecting higher porosities of the host sediment during carbonate formation. This finding is supported by lower d18O values of crusts, agreeing with precipitation from pore waters similar in composition to seawater. The aragonitic mineralogy of the crusts is also in accord with precipitation from sulfate-rich pore waters similar to seawater. Moreover, the interpretation regarding the relative depth of formation of crusts and nodules agrees with the commonly observed pattern that ANME-1 archaea tend to occur deeper in the sediment than members of the ANME-2 group. Methane represents the predominant carbon source of all carbonates (d13C values as low as -58.9 per mil V-PDB) and the encrusted archaeal biomarkers (d13C values as low as -140 per mil V-PDB). Oxygen isotope values of some nodular carbonates, ranging from + 3.9 to + 5.1per mil V-PDB, are too high for precipitation in equilibrium with seawater, probably reflecting the destabilization of gas hydrates, which are particularly abundant at the Kouilou pockmarks.

Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.