IGNNK uses GNN for spatiotemporal kriging, improving scalability and transferability.
problem Efficiently recovering signals for unsampled locations in spatiotemporal data.
method Developed an Inductive Graph Neural Network Kriging (IGNNK) model to learn spatial message passing.
result IGNNK effectively learns spatial message passing and can be transferred to new graph structures.
Kriformer uses graph transformers to estimate data in sparse sensor areas.
problem Sparse sensor deployment and unreliable data in spatiotemporal kriging tasks.
method Graph transformer model with positional encoding and attention mechanisms.
result Kriformer excels in representing unobserved locations in spatiotemporal kriging tasks.
New method improves traffic speed estimation from sparse data.
problem Incomplete and noisy traffic speed data from sparse sensors.
method Laplacian-enhanced low-rank tensor kriging (LETC) framework.
result LETC achieves state-of-the-art kriging performance under low observation rates.
New kriging method improves mean estimation and uncertainty.
problem Improving mean estimation and uncertainty in kriging.
method Proposes a rational kriging method using generalized least squares and Gaussian process.
result Generalized least squares estimate is more well-behaved than ordinary kriging.
Improved Kriging model reduces prediction errors.
problem Improving prediction accuracy in Kriging models.
method Theta-regularized Kriging model with Lasso, Ridge, and Elastic-net penalties.
result The Theta-regularized Kriging model outperforms other penalized Kriging models in accuracy and stability.
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.
problem High-dimensional function approximation for expensive models.
method Splitting training data into slices, using sliced likelihood function, and learning hyper-parameters from sensitivity indices.
result SGE-Kriging achieves comparable accuracy to standard GE-Kriging but with lower training costs.
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.
problem Improving spatial and space-time prediction accuracy.
method Combines regression trees with kriging's covariance structures.
result Treeging outperforms kriging and random forest in various scenarios.
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.
problem Predicting futures prices with trends and bid-ask spreads.
method Bayesian Kriging technique to model term structure.
result Kriging accurately predicts futures prices with embedded 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
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
New method improves stochastic kriging for high-dimensional simulations.
problem High-dimensional simulation models require prohibitive sample sizes and computational costs.
method Tensor Markov kernels and sparse grid experimental designs.
result Sample complexity grows only slightly with dimensionality, improving accuracy and efficiency.
Estimates reliability of nuclear fuel using advanced modeling techniques.
problem Determining the reliability of TRISO-coated particle fuel, which has small failure probabilities and expensive computational models.
method Coupled active learning, multifidelity modeling, and subset simulation.
result Multifidelity modeling strategies consistently reduce the number of high-fidelity model calls.
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…
Study compares geostatistical and machine learning models for PM2.5 prediction.
problem Improving accuracy of hourly PM2.5 maps across California.
method Traditional geostatistical methods (kriging, land use regression) and machine learning models (neural networks, random forests, support vector machines) were evaluated.
result Ensemble model enhanced predictive accuracy of PM2.5 concentration by correcting PurpleAir data bias.
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.
problem Spatial interpolation challenges, especially nonstationarity and lack of explanatory variables.
method Feature-Free Regression Kriging (FFRK) method that extracts geospatial features.
result FFRK outperforms classical methods in predicting heavy metal concentrations.
Deep learning improves nearshore bathymetry estimation from sparse data.
problem Estimating nearshore bathymetry from limited and often sparse data.
method Deep Neural Network (DNN) and Conditional Generative Adversarial Network (cGAN) for posterior estimates; Kriging for comparison.
result DNN-based methods outperform traditional Kriging in predicting nearshore bathymetry with sharp gradients.
DCK improves air quality index prediction with probabilistic spatial models.
problem Non-Gaussian, complex spatial structure of air quality index.
method Deep classifier kriging (DCK) for non-Gaussian, nonlinear spatial prediction.
result DCK outperforms conventional methods in predictive accuracy and uncertainty quantification.
This paper reviews spatial and spatiotemporal volatility models.
problem Capturing spatial dependence in volatility of spatial and spatiotemporal data.
method Review of time series volatility models and their extensions.
result Comparison and practical recommendations for spatial and spatiotemporal volatility models.
Bayesian method reduces misclassification errors in ranking Pareto-optimal solutions.
problem Identifying true Pareto-optimal solutions in noisy multiobjective optimization.
method Sequential allocation of extra samples using stochastic kriging to build predictive distributions.
result The proposed method outperforms existing algorithms in reducing misclassification errors.
A-BLINK speeds up Gaussian process covariance estimation.
problem Slow covariance matrix inversion in Gaussian processes.
method Two pre-trained neural networks learn Kriging weights and spatial variance.
result Significant computational speedups and posterior inference.
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.
problem Optimizing expensive functions in parallel with noisy evaluations.
method Randomized Kriging Believer (KB) based on KB heuristic.
result Randomized KB achieves Bayesian expected regret guarantees.
Bayesian deep learning improves geostatistical mapping with auxiliary data.
problem Traditional geostatistical methods are limited in feature learning and uncertainty estimation.
method Deep neural networks learn complex relationships from auxiliary data for probabilistic mapping.
result Deep learning produces detailed, probabilistic maps with uncertainty estimates.
Bayesian Complementary Kernelized Learning models complex spatiotemporal data.
problem Modeling complex, nonstationary, and nonseparable spatiotemporal data.
method Integrates kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes.
result BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates.
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 …
Dynamic model captures spatial, temporal, and spatiotemporal volatility effects.
problem Analyzing volatility in spatial and temporal networks.
method Dynamic spatiotemporal and network ARCH model with common factors, Bayesian estimation.
result Model captures strong spatial/network interactions and spillover effects.
Package {mlr3spatiotempcv} simplifies spatiotemporal resampling methods in R.
problem Assessing and tuning spatial and spatiotemporal machine learning models.
method Integrates various spatiotemporal resampling methods into the {mlr3} framework.
result Provides a consistent interface for spatiotemporal resampling methods.
BKTR models spatiotemporal data with scalable tensor regression.
problem High computational cost in applying STVC to large-scale spatiotemporal data.
method Summarize STVC coefficients in a tensor, reformulate as low-rank tensor regression, incorporate GP priors for local dependencies.
result BKTR efficiently models large spatiotemporal datasets with reduced parameters and local dependencies.
Consider a family Z={xi,yi,1≤i≤N} of N pairs of vectors xi∈Rd and scalars yi that we aim to predict for a new sample vector x0. Kriging models y as a sum of a deterministic function m, a drift which depends on the point $\boldsymbol…
New method learns spatiotemporal dynamics from random point process observations.
problem Challenges in modeling spatiotemporal dynamics from randomly collected data.
method Integration of neural differential equations, neural point processes, implicit neural representations, and amortized variational inference.
result Significant improvements in predictive accuracy and computational efficiency compared to existing methods.
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…
Chronnet models spatiotemporal data using chronological networks.
problem Handling large spatiotemporal datasets efficiently.
method Chronnet: Grid-based network model representing events chronologically.
result Chronnet captures frequent patterns, spatial changes, outliers, and clusters.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
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…
Paper uses DMD to embed time in spatiotemporal forecasting.
problem Forecasting long-range seasonal dependencies in spatiotemporal data.
method Dynamic Mode Decomposition (DMD) for time representation.
result DMD-based embedding improves long-horizon forecasting accuracy.
DeepKriging uses DNNs to predict spatial data with improved accuracy and scalability.
problem Predicting spatial processes with non-linear and non-Gaussian data.
method Adds an embedding layer of spatial coordinates with basis functions to DNNs.
result DeepKriging provides non-linear predictions with smaller approximation errors and is scalable for large datasets.
This paper surveys differential privacy methods for transportation spatiotemporal data.
problem Protecting user privacy in public release of spatiotemporal data.
method Review of differential privacy mechanisms and their application in transportation.
result Challenges in deploying and adopting differential privacy in transportation.
GATGPT uses LLMs with graph attention for spatiotemporal data imputation.
problem Missing values in spatiotemporal data due to sensor malfunctions and data transmission errors.
method Integrates pre-trained large language models with graph attention mechanisms.
result GATGPT achieves comparable results to deep learning benchmarks on real-world datasets.
New unsupervised transfer learning method for spatiotemporal tasks.
problem Transfer knowledge from unsupervised models to new predictive tasks.
method Differentiable framework with Transferable Memory Unit (TMU).
result Significant improvements on spatiotemporal prediction benchmarks.
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…
This paper proposes a geometry-aware active learning framework for spatiotemporal dynamic systems.
problem Challenges in modeling complex dynamic systems with 3D geometries and time evolution.
method Geometry-aware spatiotemporal Gaussian Process (G-ST-GP) and adaptive active learning strategy.
result The proposed framework outperforms traditional methods in predicting high-dimensional dynamic behaviors.