arXiv research

New kriging method improves mean estimation and uncertainty.

Improved Kriging model reduces prediction errors.

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bott…

SGE-Kriging reduces high-dimensional surrogate modelling costs.

IGNNK uses GNN for spatiotemporal kriging, improving scalability and transferability.

Recently, a lot of effort has been paid to the efficient computation of Kriging predictors when observations are assimilated sequentially. In particular, Kriging update formulae enabling significant computational savings were derived in Barnes and Watson (1992), Gao et al. (1996), and Emery (2009). Taking advantage of …

Treeging combines regression trees and kriging for spatial and space-time prediction.

We propose an extension of the concept of Expected Improvement criterion commonly used in Kriging based optimization. We extend it for more complex Kriging models, e.g. models using derivatives. The target field of application are CFD problems, where objective function are extremely expensive to evaluate, but the theor…

Kriging predicts futures prices by accounting for trends and bid-ask spreads.

The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a sufficient metamodel should be kept low, which can be achieved by using adaptive…

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 models (a.k.a meta-models) have been increasingly investigated in the last decade.…

Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation

New method improves stochastic kriging for high-dimensional simulations.

Estimates reliability of nuclear fuel using advanced modeling techniques.

New method improves traffic speed estimation from sparse data.

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers of observations present makes it inefficient to apply full Kriging. In order to r…

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomia…

We investigate two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz. First, we propose the use of stochastic kriging (Gaussian process) meta-models for fitting the continuation value. Kriging offers a flexible, nonparametr…

FFRK automatically extracts features for spatial interpolation without external variables.

Deep learning improves nearshore bathymetry estimation from sparse data.

Kriformer uses graph transformers to estimate data in sparse sensor areas.

DCK improves air quality index prediction with probabilistic spatial models.

Bayesian method reduces misclassification errors in ranking Pareto-optimal solutions.

A-BLINK speeds up Gaussian process covariance estimation.

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 b…

Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large number of function evaluations. Gradient-enhanced kriging has the potential to r…

Proposes a new PBO method with theoretical guarantees.

Bayesian deep learning improves geostatistical mapping with auxiliary data.

We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000). Our method can handle general discontinuous cross-correlations among systems with different levels of fidelity. A combination of multi-fidelity Gaussian Processes (AR(1) Co-kriging) and …

Consider a family $Z=\{\boldsymbol{x_{i}},y_{i}$,$1\leq i\leq N\}$ of $N$ pairs of vectors $\boldsymbol{x_{i}} \in \mathbb{R}^d$ and scalars $y_{i}$ that we aim to predict for a new sample vector $\mathbf{x}_0$. Kriging models $y$ as a sum of a deterministic function $m$, a drift which depends on the point $\boldsymbol…

The hedonic approach based on a regression model has been widely adopted for the prediction of real estate property price and rent. In particular, a spatial regression technique called Kriging, a method of interpolation that was advanced in the field of spatial statistics, are known to enable high accuracy prediction i…

This work explores variably scaled kernels to improve non-stationary Gaussian processes.

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 covariance kernels when the dimension of input increases. In oder to get round the cu…

DeepKriging uses DNNs to predict spatial data with improved accuracy and scalability.

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probab…

A new method optimizes complex engineering designs under uncertainty efficiently.

The article proposes optimal learning strategies for machine learning-based reliability analysis.

Study improves sugarcane plot prediction using data interpolation.

Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and stationarity. We propose a more flexible spatial prediction method based on the Nearest-Neig…

Improved spatial prediction for massive datasets using SME model.

In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…

Novel neural GP kernels learn stable, flexible covariance structures.

Kriging is an efficient machine-learning tool, which allows to obtain an approximate response of an investigated phenomenon on the whole parametric space. Adaptive schemes provide a the ability to guide the experiment yielding new sample point positions to enrich the metamodel. Herein a novel adaptive scheme called Mon…

Large uncertainties in many phenomena have challenged decision making. Collecting additional information to better characterize reducible uncertainties is among decision alternatives. Value of information (VoI) analysis is a mathematical decision framework that quantifies expected potential benefits of new data and ass…

Neural networks improve geospatial data analysis by relaxing linearity assumptions.

A new method for high-dimensional RBDO using stochastic emulators.

Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The prop…

The Efficient Global Optimization (EGO) algorithm uses a conditional Gaus-sian Process (GP) to approximate an objective function known at a finite number of observation points and sequentially adds new points which maximize the Expected Improvement criterion according to the GP. The important factor that controls the e…