We study posterior rates of contraction in Gaussian process regression with potentially unbounded covariate domain. Our argument relies on developing a Gaussian approximation to the posterior of the leading coefficients of a Karhunen–Loève expansion of the Gaussian process. The salient feature of our result is deriving such an approximation in the L2 Wasserstein distance and relating the speed ...

Gaussian process (GP) regression used for forecasting battery state of

In the context of expensive numerical experiments, a promising solution to alleviate the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at a price of precision in the response. This work addresses the issue of fitting a Gaussian process metamodel to partially converged simulation data, for further use in predic...

The paper deals with the application of the theory of locally homogeneous and isotropic Gaussian fields (LHIGF) to probabilistic modelling of multivariate data structures. An asymptotic model is also studied, when the correlation function parameter of the Gaussian field tends to infinity. The kriging procedure is developed which presents a simple extrapolator by means of a matrix of degrees of ...

ABSTRACT Kriging is a popular analysis approach for computer experiment for the purpose of creating a cheap-to-compute "metamodel" as a surrogate to a computationally expensive engineering simulation model. The maximum likelihood approach is employed to estimate the parameters in the Kriging model. However, the likelihood function near the optimum may be flat in some situations, and this leads ...

This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function. The Kriging interpolation technique (or Gaussian process regression) is often considered to tackle such a problem but the method suffers from its computational burden when the number of observation points is large. We introduce in this ar...

We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabi...

Sequential parameter optimization is a heuristic that combines classical and modern statistical techniques to improve the performance of search algorithms. It includes methods for tuning based on classical regression and analysis of variance techniques; tree-based models such as CART and random forest; Gaussian process models (Kriging), and combinations of different meta-modeling approaches. Th...

We consider an off-line process design problem where the response variable is affected by several factors. We present a data-based modelling approach that iteratively allocates new experimental points, update the model, and search for the optimal process factors. A flexible non-linear modelling technique, the kriging (also known as Gaussian processes), forms the cornerstone of this approach. Kr...

This paper presents an automated method for creating spatial maps of soil condition with an outdoor mobile robot. Effective soil mapping on farms can enhance yields, reduce inputs and help protect the environment. Traditionally, data are collected manually at an arbitrary set of locations, then soil maps are constructed offline using Kriging, a form of Gaussian process regression. This process ...