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.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
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…
New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.
problem Non-stationary spatial modelling with multiple secondary variables.
method Combines Geostatistics and Quantile Random Forests to estimate conditional distributions and simulate spatial data.
result Consistent results similar to geostatistical and Quantile Random Forests, allowing for embedding simpler interpolation techniques.
Deep learning extracts terrain texture covariates for geostatistical modeling.
problem Improving prediction accuracy in geostatistical modeling using terrain texture data.
method Deep learning approach to automatically derive optimal terrain texture covariates from SRTM 90m DEM.
result Deep learning-derived covariates have strong explanatory power (R-squared around 0.6) for geochemical data.
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.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness…
Geostatistical learning faces unique challenges due to spatial correlation and covariate shifts.
problem Challenges in applying statistical learning to geospatial data.
method Assessing generalization error under covariate shift and spatial correlation.
result No classical learning methods are adequate for model selection in geospatial contexts.
Soil organic carbon (SOC) plays a major role in the global carbon budget. It can act as a source or a sink of atmospheric carbon, thereby possibly influencing the course of climate change. Improving the tools that model the spatial distributions of SOC stocks at national scales is a priority, both for monitoring change…
Adaptive LASSO improves model selection for functional geostatistical data.
problem Modeling georeferenced data with spatiotemporal dynamics and functional coefficients.
method Penalized maximum likelihood estimator with adaptive LASSO penalty for simultaneous selection of spline basis functions and regressors.
result The penalized estimator outperforms the unpenalized estimator in all scenarios tested.
Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purp…
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 methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
The paper builds interpretable models for property markets using machine learning.
problem Noise in real market data and differences from ideal data.
method Combining classical linear regression with kriging for land parcels, and RuleFit method for flats.
result Effective models can be built for property markets while maintaining interpretability.
CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
A new model predicts financial volatility across firms using spatial correlations.
problem Predicting financial volatility across firms in a network.
method Heterogeneous spatiotemporal GARCH model with local likelihood estimation.
result The model captures spatial spillovers and contagion effects in financial networks.
SAGE generates subsurface velocity models from sparse well logs and seismic images.
problem Lack of high-quality subsurface velocity models due to limited data availability.
method Subsurface AI-driven geostatistical extraction using proxy posterior.
result SAGE produces geologically plausible and statistically accurate velocity realizations.
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …
Probabilistic inversion within a multiple-point statistics framework is often computationally prohibitive for high-dimensional problems. To partly address this, we introduce and evaluate a new training-image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generat…
Dual random fields improve mineral potential predictions.
problem Limited understanding of multi-dimensional causalities and dependencies.
method Introduces dual random fields to pool response functions across the domain.
result Spatial inference and uncertainty assessment of response models and predictions.
The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine le…
GeoConformal predicts spatial uncertainty without relying on specific models.
problem Measuring uncertainty in spatial predictions to enhance model credibility.
method GeoConformal Prediction integrates geographical weighting into conformal prediction.
result GeoConformal achieves higher coverage rates in uncertainty assessment compared to Bootstrap methods.
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feas…
An important problem in geostatistics is to build models of the subsurface of the Earth given physical measurements at sparse spatial locations. Typically, this is done using spatial interpolation methods or by reproducing patterns from a reference image. However, these algorithms fail to produce realistic patterns and…
Geostatistical modeling of petrophysical properties is a key step in modern integrated oil and gas reservoir studies. Recently, generative adversarial networks (GAN) have been shown to be a successful method for generating unconditional simulations of pore- and reservoir-scale models. This contribution leverages the di…
Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While …
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
A new Latent Diffusion Model generates realistic reservoir facies.
problem Creating accurate reservoir facies from limited measurements.
method Proposes a Latent Diffusion Model for conditional facies generation.
result Significantly outperforms GAN-based alternatives in fidelity and realism.
Efficiently analyzes multidimensional functional data using separable basis functions.
problem Curse of dimensionality in traditional functional data analysis.
method Marginal product basis systems for multidimensional data, tensor decomposition, differential operator-based penalties.
result Efficient estimation of multidimensional functional data representations.
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.
The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to as "history matching", can be formalised as an ill-posed inverse pr…
Develops Gaussian processes on non-Euclidean spaces with symmetries.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes on compact and non-compact spaces.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Develops Gaussian processes on non-compact Lie groups.
problem Invariance to symmetries in non-Euclidean spaces.
method Constructive techniques for stationary Gaussian processes.
result Makes non-Euclidean Gaussian processes compatible with standard software.
Combining deep learning and ensemble smoothers for better history matching.
problem Dealing with complex facies distributions in history matching.
method Using autoencoders and generative adversarial networks to parameterize facies models, applying distance-based localization.
result Improved history matching performance with deep learning parameterizations.
Neural networks improve geospatial data analysis by relaxing linearity assumptions.
problem Traditional geospatial analysis assumes linear models, limiting flexibility.
method Embedding neural networks within traditional geostatistical models for non-linear mean functions.
result NN-GLS algorithm provides consistent and scalable predictions for irregular spatial data.
FNO model predicts GCS pressure fields with 81% less data, even with limited high-fidelity data.
problem Accurate prediction of complex physical behaviors in large-scale 3D geological carbon storage problems with limited data.
method Multi-fidelity Fourier Neural Operator (FNO) for efficient training with multi-fidelity datasets.
result Multi-fidelity FNO model predicts pressure fields with reasonable accuracy even with limited high-fidelity data.
A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in computer vision using deep learning. CNN-PCA can be viewed as a generalization of an ex…