Related papers: DeepKriging: Spatially Dependent Deep Neural Netwo…

Kriging is a widely employed technique, in particular for computer experiments, in machine learning or in geostatistics. An important challenge for Kriging is the computational burden when the data set is large. This article focuses on a…

We propose a novel single-image super-resolution approach based on the geostatistical method of kriging. Kriging is a zero-bias minimum-variance estimator that performs spatial interpolation based on a weighted average of known…

Kriging is an established methodology for predicting spatial data in geostatistics. Current kriging techniques can handle linear dependencies on spatially referenced covariates. Although splines have shown promise in capturing nonlinear…

Accurate prediction of spatially dependent functional data is critical for various engineering and scientific applications. In this study, a spatial functional deep neural network model was developed with a novel non-linear modeling…

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…

Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically…

Multivariate measurements taken at irregularly sampled locations are a common form of data, for example in geochemical analysis of soil. In practical considerations predictions of these measurements at unobserved locations are of great…

For geospatial modelling and mapping tasks, variants of kriging - the spatial interpolation technique developed by South African mining engineer Danie Krige - have long been regarded as the established geostatistical methods. However,…

Spatio-temporal graph neural networks (STGNN) have emerged as the dominant model for spatio-temporal graph (STG) forecasting. Despite their success, they fail to model intrinsic uncertainties within STG data, which cripples their…

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…

Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict…

An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

Deep Neural Networks (DNNs) are a promising tool for Global Navigation Satellite System (GNSS) positioning in the presence of multipath and non-line-of-sight errors, owing to their ability to model complex errors using data. However,…

Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…

Approximation of functions satisfying partial differential equations (PDEs) is paramount for simulation of physical fluid flows and other problems in physics. Recently, physics-informed machine learning approaches have proven useful as a…

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…

Given coarser-resolution projections from global climate models or satellite data, the downscaling problem aims to estimate finer-resolution regional climate data, capturing fine-scale spatial patterns and variability. Downscaling is any…

In this article, we review and compare a number of methods of spatial prediction. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition…

Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…