Related papers: Rapid Approximation Prediction for Kriging

Assume that a Gaussian process $\xi$ is predicted from $n$ pointwise observations by intrinsic Kriging and that the volume of the excursion set of $\xi$ above a given threshold $u$ is approximated by the volume of the predictor. The first…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate…

Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for…

The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the…

Numerical simulation is powerful to study nonlinear solid mechanics problems. However, mesh-based or particle-based numerical methods suffer from the common shortcoming of being time-consuming, particularly for complex problems with…

Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

In the present work, we consider multi-fidelity surrogate modelling to fuse the output of multiple aero-servo-elastic computer simulators of varying complexity. In many instances, predictions from multiple simulators for the same quantity…

Quantification of uncertainty in production/injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and…

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

In the framework of the supervised learning of a real function defined on a space X , the so called Kriging method stands on a real Gaussian field defined on X. The Euclidean case is well known and has been widely studied. In this paper, we…

Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios,…

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods…

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of…