A new method for large-scale GP regression using seamless patching of local models.
problem Boundary discontinuity issue in local partitioned GP models.
method Partitioning input domain into local regions, applying different local GP models, and ensuring seamless patching with pseudo-observations.
result Mitigates boundary discontinuity problem, leading to improved accuracy and predictive uncertainty.
New method uses patchworking to represent oriented matroids.
problem Representing oriented matroids from polyhedral structures.
method Variant of Viro's patchworking, controlled cell merging process.
result Achieved a combinatorial manifestation of patchworking.
New Alexandrov-Patchwork construction for Lorentzian spaces with curvature bounds.
problem Understanding finite diameter constraints in Lorentzian geometry.
method Constructing Alexandrov-Patchwork and proving Bonnet-Myers theorem for Lorentzian spaces.
result Lorentzian spaces with curvature bounds have finite diameter.
Cluster Quilting clusters fragmented data sets for neuroscience and genomics.
problem Clustering fragmented data sets in neuroscience and genomics.
method Cluster Quilting method using patch ordering, patchwise SVD, sequential linear mapping, and k-means.
result Cluster Quilting discovers more accurate clusters than other methods.
A cumbersome hypothesis for Viro patchworking of real algebraic curves is the convexity of the given subdivision. It is an open question in general to know whether the convexity is necessary. In the case of trigonal curves we interpret Viro method in terms of dessins d'enfants. Gluing the dessins d'enfants in a coheren…
The study builds families of polynomials with a specific number of special parabolic points.
problem Finding polynomials with a given number of special parabolic points.
method Viro's patchworking theorem to construct families of polynomials.
result Built a family of degree d polynomials with (d−4)(2d−9) special parabolic points. 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.
New method for constructing real algebraic surfaces from complex tropical hypersurfaces.
problem Constructing real algebraic surfaces from complex tropical hypersurfaces.
method Non-Abelian patchworking theory.
result The method reproduces all existing isotopy types of surfaces up to degree three.
Paper proposes a copula method to generate unfavorable VaR scenarios.
problem Creating unfavorable VaR scenarios for insurance models.
method Patchwork copulas to create unfavorable VaR scenarios with given marginal distributions.
result Demonstrated with a 19-dimensional real-life insurance losses data set.
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…
Cluster-based Kriging reduces computational complexity for large datasets.
problem High computational and space complexity of Kriging with increasing data.
method Partition data into clusters, build multiple Kriging models.
result Proposed algorithms outperform existing methods consistently.
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.
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.
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.
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.
This thesis explores adaptive sampling techniques for creating efficient surrogate models.
problem High computational cost of numerical simulations.
method Adaptive sampling techniques for Kriging metamodels.
result Comprehensive comparison of adaptive sampling techniques for Kriging.
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.
Classifies real algebraic curves on a quadric ellipsoid of specific degree.
problem Classifying real algebraic curves of bidegree (5,5) on the quadric ellipsoid.
method Reduction to curves in the second Hirzebruch surface, combining classical construction methods on toric surfaces.
result Previously known restrictions form a complete system for this bidegree.
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
Nested Kriging improves prediction for large datasets.
problem Predicting function values from limited observations.
method Aggregating sub-models based on subsets of observation points.
result The proposed method is consistent and outperforms other aggregation methods.
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.
The paper explores efficient global optimization using Kriging models.
problem Optimizing complex functions with limited evaluations.
method Implemented UK-EGO framework with automatic trend function selection.
result PCK-EGO variant showed the best performance.
A new method for regression and classification using zonal kriging.
problem Predicting scalar values from vector inputs using kriging models.
method Constructing an unbiased estimator using zonality hypothesis and kriging.
result An explicit closed-form solution for the coefficients with minimal variance.
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.
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.
Study compares Kriging and DNN for apartment rent price prediction accuracy.
problem Comparing predictive accuracy of Kriging and DNN for apartment rent prices.
method Used Kriging and DNN models on large datasets (n = 10^4, 10^5, 10^6).
result DNN outperforms NNGP as sample size increases, especially for higher and lower end properties.
Gradient-enhanced kriging reduces function evaluations for high-dimensional problems.
problem High-dimensional function evaluations are computationally expensive.
method Developed a new gradient-enhanced surrogate model using partial-least squares to reduce hyperparameters and correlation matrix size.
result Significantly reduces the number of function evaluations required for accurate surrogate models.
A new adaptive kriging method improves binary classification of mechanical problems.
problem Efficient binary classification of mechanical problems with high fluctuation.
method Monte Carlo-intersite Voronoi (MiVor) adaptive scheme for regression surrogate model.
result The MiVor algorithm provides accurate binary classification with fewer observation points for highly fluctuating response surfaces.
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…
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.
A new geostatistical model using deep learning for spatial prediction.
problem Traditional kriging assumptions and limitations.
method Nearest-Neighbor Neural Network (4N) process integrating deep learning.
result 4N process outperforms existing geostatistical methods for non-Gaussian data.
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.
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.
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 paper proposes a new VoI analysis framework for complex decision problems.
problem Optimizing resource allocation for information collection in decision-making under uncertainty.
method Surrogate-based framework for Value of Information analysis, integrating knowledge sharing and adaptive training.
result Accurate and robust estimates of VoI with fewer model evaluations compared to state-of-the-art methods.
Combines low-fidelity and high-fidelity labels using Gaussian process co-kriging.
problem Classification with variable fidelity labels.
method Gaussian process co-kriging for latent functions, extended Laplace inference for multi-fidelity data.
result More resistant to labeling discrepancy than other fusion methods.
A new method for optimizing using ensembles of kriging models.
problem Optimizing using traditional Gaussian Process (GP) methods is computationally expensive and may not be the most efficient approach.
method Proposes a novel approach where at each iteration, a small ensemble of kriging models with different length-scales is created and used to produce an iterate.
result The method shows potential for parallel implementations but does not perform better than classical EGO in a sequential context.
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.
PhIK uses physics models to improve Gaussian process regression.
problem Improving Gaussian process regression for complex systems.
method Constructs non-stationary Gaussian processes from physics models, avoiding hyperparameter optimization.
result Guaranteed physical constraints in predictions and error estimates.
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…