Accurate spatial interpolation of the air quality index (AQI), computed from concentrations of multiple air pollutants, is essential for regulatory decision-making, yet AQI fields are inherently non-Gaussian and often exhibit complex nonlinear spatial structure. Classical spatial prediction methods such as kriging are linear and rely on Gaussian assumptions, which limits their ability to capture these features and to provide reliable predictive distributions. In this study, we propose \textit{deep classifier kriging} (DCK), a flexible, distribution-free deep learning framework for estimating full predictive distribution functions for univariate and bivariate spatial processes, together with a \textit{data fusion} mechanism that enables modeling of non-collocated bivariate processes and integration of heterogeneous air pollution data sources. Through extensive simulation experiments, we show that DCK consistently outperforms conventional approaches in predictive accuracy and uncertainty quantification. We further apply DCK to probabilistic spatial prediction of AQI by fusing sparse but high-quality station observations with spatially continuous yet biased auxiliary model outputs, yielding spatially resolved predictive distributions that support downstream tasks such as exceedance and extreme-event probability estimation for regulatory risk assessment and policy formulation.

Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond achieving higher accuracy, it is equally important to obtain predictions with uncertainty measures to enhance model credibility and support responsible spatial prediction. Although geostatistic methods like Kriging offer some level of uncertainty assessment, such as Kriging variance, these measurements are not always accurate and lack general applicability to other spatial models. To address this issue, we propose a model-agnostic uncertainty assessment method called GeoConformal Prediction, which incorporates geographical weighting into conformal prediction. We applied it to two classic spatial prediction cases, spatial regression and spatial interpolation, to evaluate its reliability. First, in the spatial regression case, we used XGBoost to predict housing prices, followed by GeoConformal to calculate uncertainty. Our results show that GeoConformal achieved a coverage rate of 93.67%, while Bootstrap methods only reached a maximum coverage of 81.00% after 2000 runs. Next, we applied GeoConformal to spatial interpolation models. We found that the uncertainty obtained from GeoConformal aligned closely with the variance in Kriging. Finally, using GeoConformal, we analyzed the sources of uncertainty in spatial prediction. We found that explicitly including local features in AI models can significantly reduce prediction uncertainty, especially in areas with strong local dependence. Our findings suggest that GeoConformal holds potential not only for geographic knowledge discovery but also for guiding the design of future GeoAI models, paving the way for more reliable and interpretable spatial prediction frameworks.

Spatial data is ubiquitous, encompassing a wide range of applications from environmental observations and biological measurements to more recent fields like computer vision. A critical challenge in the analysis of spatial data is spatial prediction, which involves estimating unobserved values based on nearby observations under the assumption of certain correlations. Among parametric algorithms, Kriging is particularly notable ((Matheron (1963))). Described as the best linear unbiased estimator (BLUE), Kriging employs a weighted average of nearby observations, with weights determined by a covariance function typically presumed to be stationary. However, this assumption does not hold in many real-world scenarios, such as data from satellites, monitoring stations, and urban streets, which tend to exhibit nonstationarity (Katzfuss (2013)).

One key task in environmental science is to map environmental variables continuously in space or even in space and time. Machine learning algorithms are frequently used to learn from local field observations to make spatial predictions by estimating the value of the variable of interest in places where it has not been measured. However, the application of machine learning strategies for spatial mapping involves additional challenges compared to "non-spatial" prediction tasks that often originate from spatial autocorrelation and from training data that are not independent and identically distributed. In the past few years, we developed a number of methods to support the application of machine learning for spatial data which involves the development of suitable cross-validation strategies for performance assessment and model selection, spatial feature selection, and methods to assess the area of applicability of the trained models. The intention of the CAST package is to support the application of machine learning strategies for predictive mapping by implementing such methods and making them available for easy integration into modelling workflows. Here we introduce the CAST package and its core functionalities. At the case study of mapping plant species richness, we will go through the different steps of the modelling workflow and show how CAST can be used to support more reliable spatial predictions.

With the rise of electronic data, particularly Earth observation data, data-based geospatial modelling using machine learning (ML) has gained popularity in environmental research. Accurate geospatial predictions are vital for domain research based on ecosystem monitoring and quality assessment and for policy-making and action planning, considering effective management of natural resources. The accuracy and computation speed of ML has generally proved efficient. However, many questions have yet to be addressed to obtain precise and reproducible results suitable for further use in both research and practice. A better understanding of the ML concepts applicable to geospatial problems enhances the development of data science tools providing transparent information crucial for making decisions on global challenges such as biosphere degradation and climate change. This survey reviews common nuances in geospatial modelling, such as imbalanced data, spatial autocorrelation, prediction errors, model generalisation, domain specificity, and uncertainty estimation. We provide an overview of techniques and popular programming tools to overcome or account for the challenges. We also discuss prospects for geospatial Artificial Intelligence in environmental applications. To date, obtaining spatial predictions is an essential step in the monitoring, assessment, and prognosis tasks applicable to all kinds of Earth systems on both local and global scales (Figure 1).

Spatial prediction of the radio propagation environment of a transmitter can assist and improve various aspects of wireless networks. The majority of research in this domain can be categorized as 'reactive' spatial prediction, where the predictions are made based on a small set of measurements from an active transmitter whose radio environment is to be predicted. Emerging spectrum-sharing paradigms would benefit from 'proactive' spatial prediction of the radio environment, where the spatial predictions must be done for a transmitter for which no measurement has been collected. This paper proposes a novel, supervised deep learning-based framework, ProSpire, that enables spectrum sharing by leveraging the idea of proactive spatial prediction. We carefully address several challenges in ProSpire, such as designing a framework that conveniently collects training data for learning, performing the predictions in a fast manner, enabling operations without an area map, and ensuring that the predictions do not lead to undesired interference. ProSpire relies on the crowdsourcing of transmitters and receivers during their normal operations to address some of the aforementioned challenges. The core component of ProSpire is a deep learning-based image-to-image translation method, which we call RSSu-net. We generate several diverse datasets using ray tracing software and numerically evaluate ProSpire. Our evaluations show that RSSu-net performs reasonably well in terms of signal strength prediction, 5 dB mean absolute error, which is comparable to the average error of other relevant methods. Importantly, due to the merits of RSSu-net, ProSpire creates proactive boundaries around transmitters such that they can be activated with 97% probability of not causing interference. In this regard, the performance of RSSu-net is 19% better than that of other comparable methods.

High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Mat\'ern covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.

With increasing number of crowdsourced private automatic weather stations (called TPAWS) established to fill the gap of official network and obtain local weather information for various purposes, the data quality is a major concern in promoting their usage. Proper quality control and assessment are necessary to reach mutual agreement on the TPAWS observations. To derive near real-time assessment for operational system, we propose a simple, scalable and interpretable framework based on AI/Stats/ML models. The framework constructs separate models for individual data from official sources and then provides the final assessment by fusing the individual models. The performance of our proposed framework is evaluated by synthetic data and demonstrated by applying it to a re-al TPAWS network.

Inverse Distance Weighted models (IDW) have been widely used for predicting and modeling multidimensional space in multimodal industrial processes. However, the more complex the structure of multidimensional space, the lower the performance of IDW models, and real industrial datasets tend to have more complex spatial structure. To solve this problem, a new framework for spatial prediction and modeling based on deep reinforcement learning network is proposed. In the proposed framework, the internal relationship between state and action is enhanced by reusing the state values in the Q network, and the convergence rate and stability of the deep reinforcement learning network are improved. The improved deep reinforcement learning network is then used to search for and learn the hyperparameters of each sample point in the inverse distance weighted model. These hyperparameters can reflect the spatial structure of the current industrial dataset to some extent. Then a spatial distribution of hyperparameters is constructed based on the learned hyperparameters. Each interpolation point obtains corresponding hyperparameters from the hyperparametric spatial distribution and brings them into the classical IDW models for prediction, thus achieving differential spatial prediction and modeling. The simulation results show that the proposed framework is suitable for real industrial datasets with complex spatial structure characteristics and is more accurate than current IDW models in spatial prediction.

In spatial statistics, a common objective is to predict the values of a spatial process at unobserved locations by exploiting spatial dependence. In geostatistics, Kriging provides the best linear unbiased predictor using covariance functions and is often associated with Gaussian processes. However, when considering non-linear prediction for non-Gaussian and categorical data, the Kriging prediction is not necessarily optimal, and the associated variance is often overly optimistic. We propose to use deep neural networks (DNNs) for spatial prediction. Although DNNs are widely used for general classification and prediction, they have not been studied thoroughly for data with spatial dependence. In this work, we propose a novel neural network structure for spatial prediction by adding an embedding layer of spatial coordinates with basis functions. We show in theory that the proposed DeepKriging method has multiple advantages over Kriging and classical DNNs only with spatial coordinates as features. We also provide density prediction for uncertainty quantification without any distributional assumption and apply the method to PM$_{2.5}$ concentrations across the continental United States.