Accurate acquisition of high-resolution surface meteorological conditions is critical for forecasting and simulating meteorological variables. Directly applying spatial interpolation methods to derive meteorological values at specific locations from low-resolution grid fields often yields results that deviate significantly from the actual conditions. Existing downscaling methods primarily rely on the coupling relationship between geostationary satellites and ERA5 variables as a condition. However, using brightness temperature data from geostationary satellites alone fails to comprehensively capture all the changes in meteorological variables in ERA5 maps. To address this limitation, we can use a wider range of satellite data to make more full use of its inversion effects on various meteorological variables, thus producing more realistic results across different meteorological variables. To further improve the accuracy of downscaling meteorological variables at any location, we propose the Multi-source Observation Down-Scaling Model (MODS). It is a conditional diffusion model that fuses data from multiple geostationary satellites GridSat, polar-orbiting satellites (AMSU-A, HIRS, and MHS), and topographic data (GEBCO), as conditions, and is pre-trained on the ERA5 reanalysis dataset. During training, latent features from diverse conditional inputs are extracted separately and fused into ERA5 maps via a multi-source cross-attention module. By exploiting the inversion relationships between reanalysis data and multi-source atmospheric variables, MODS generates atmospheric states that align more closely with real-world conditions. During sampling, MODS enhances downscaling consistency by incorporating low-resolution ERA5 maps and station-level meteorological data as guidance. Experimental results demonstrate that MODS achieves higher fidelity when downscaling ERA5 maps to a 6.25 km resolution.
Evaluating foundation models for crystallographic reasoning requires benchmarks that isolate generalization behavior while enforcing physical constraints. This work introduces a multiscale multicrystal dataset with two physically grounded evaluation protocols to stress-test multimodal generative models. The Spatial-Exclusion benchmark withholds all supercells of a given radius from a diverse dataset, enabling controlled assessments of spatial interpolation and extrapolation. The Compositional-Exclusion benchmark omits all samples of a specific chemical composition, probing generalization across stoichiometries. Nine vision--language foundation models are prompted with crystallographic images and textual context to generate structural annotations. Responses are evaluated via (i) relative errors in lattice parameters and density, (ii) a physics-consistency index penalizing volumetric violations, and (iii) a hallucination score capturing geometric outliers and invalid space-group predictions. These benchmarks establish a reproducible, physically informed framework for assessing generalization, consistency, and reliability in large-scale multimodal models. Dataset and code are available at https://github.com/KurbanIntelligenceLab/StressTestingMMFMinCR.
The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic nature of our system, this assumption is complicated by sensitive dependence, where small uncertainties in initial conditions can lead to exponentially diverging outcomes over time. This challenge is particularly salient at global spatial scales and over centennial timescales, where data gaps are not just common but expected. The source of uncertainty is two-fold: (1) sparse, noisy observations from satellites and ground stations, and (2) internal variability stemming from the simplifying approximations within the models themselves. In practice, data assimilation methods are used to reconcile this missing information by conditioning model states on partial observations. Our work builds on this idea but operates at the extreme end of sparsity. We propose a conditional data imputation framework that reconstructs full temperature fields from as little as 1% observational coverage. The method leverages a diffusion model guided by a prekriged mask, effectively inferring the full-state fields from minimal data points. We validate our framework over the Southern Great Plains, focusing on afternoon (12:00-6:00 PM) temperature fields during the summer months of 2018-2020. Across varying observational densities--from swath data to isolated in-situ sensors--our model achieves strong reconstruction accuracy, highlighting its potential to fill in critical data gaps in both historical reanalysis and real-time forecasting pipelines.
Asymmetric, non-Gaussian probability distributions are often observed in the analysis of natural and engineering datasets. The lognormal distribution is a standard model for data with skewed frequency histograms and fat tails. However, the lognormal law severely restricts the asymptotic dependence of the probability density and the hazard function for high values. Herein we present a family of three-parameter non-Gaussian probability density functions that are based on generalized kappa-exponential and kappa-logarithm functions and investigate its mathematical properties. These kappa-lognormal densities represent continuous deformations of the lognormal with lighter right tails, controlled by the parameter kappa. In addition, bimodal distributions are obtained for certain parameter combinations. We derive closed-form analytic expressions for the main statistical functions of the kappa-lognormal distribution. For the moments, we derive bounds that are based on hypergeometric functions as well as series expansions. Explicit expressions for the gradient and Hessian of the negative log-likelihood are obtained to facilitate numerical maximum-likelihood estimates of the kappa-lognormal parameters from data. We also formulate a joint probability density function for kappa-lognormal stochastic processes by applying Jacobi's multivariate theorem to a latent Gaussian process. Estimation of the kappa-lognormal distribution based on synthetic and real data is explored. Furthermore, we investigate applications of kappa-lognormal processes with different covariance kernels in time series forecasting and spatial interpolation using warped Gaussian process regression. Our results are of practical interest for modeling skewed distributions in various scientific and engineering fields.
Accurate acquisition of surface meteorological conditions at arbitrary locations holds significant importance for weather forecasting and climate simulation. Due to the fact that meteorological states derived from satellite observations are often provided in the form of low-resolution grid fields, the direct application of spatial interpolation to obtain meteorological states for specific locations often results in significant discrepancies when compared to actual observations. Existing downscaling methods for acquiring meteorological state information at higher resolutions commonly overlook the correlation with satellite observations. To bridge the gap, we propose Satellite-observations Guided Diffusion Model (SGD), a conditional diffusion model pre-trained on ERA5 reanalysis data with satellite observations (GridSat) as conditions, which is employed for sampling downscaled meteorological states through a zero-shot guided sampling strategy and patch-based methods. During the training process, we propose to fuse the information from GridSat satellite observations into ERA5 maps via the attention mechanism, enabling SGD to generate atmospheric states that align more accurately with actual conditions. In the sampling, we employed optimizable convolutional kernels to simulate the upscale process, thereby generating high-resolution ERA5 maps using low-resolution ERA5 maps as well as observations from weather stations as guidance. Moreover, our devised patch-based method promotes SGD to generate meteorological states at arbitrary resolutions. Experiments demonstrate SGD fulfills accurate meteorological states downscaling to 6.25km.
This paper introduces a noise-tolerant computing method for over-the-air computation (AirComp) aimed at weighted averaging, which is critical in various Internet of Things (IoT) applications such as environmental monitoring. Traditional AirComp approaches, while efficient, suffer significantly in accuracy due to noise enhancement in the normalization by the sum of weights. Our proposed method allows nodes to adaptively truncate their weights based on the channel conditions, thereby enhancing noise tolerance. Applied to distributed Gaussian process regression (D-GPR), the method facilitates low-latency, low-complexity, and high-accuracy distributed regression across a range of signal-to-noise ratios (SNRs). We evaluate the performance of the proposed method in a radio map construction problem, which involves visualizing the radio environment based on limited sensing information and spatial interpolation. Numerical results show that our approach maintains computational accuracy in low-SNR scenarios and achieves performance close to ideal conditions in high SNR environments. In addition, a case study targeting a federated learning (FL) system demonstrates the potential of our proposed method in improving model aggregation accuracy, not only for D-GPR but also for FL systems.
Generating continuous environmental models from sparsely sampled data is a critical challenge in spatial modeling, particularly for topography. Traditional spatial interpolation methods often struggle with handling sparse measurements. To address this, we propose a Transformer-based Generative Model for Spatial Interpolation (T-GMSI) using a vision transformer (ViT) architecture for digital elevation model (DEM) generation under sparse conditions. T-GMSI replaces traditional convolution-based methods with ViT for feature extraction and DEM interpolation while incorporating a terrain feature-aware loss function for enhanced accuracy. T-GMSI excels in producing high-quality elevation surfaces from datasets with over 70% sparsity and demonstrates strong transferability across diverse landscapes without fine-tuning. Its performance is validated through extensive experiments, outperforming traditional methods such as ordinary Kriging (OK) and natural neighbor (NN) and a conditional generative adversarial network (CGAN)-based model (CEDGAN). Compared to OK and NN, T-GMSI reduces root mean square error (RMSE) by 40% and 25% on airborne lidar data and by 23% and 10% on spaceborne lidar data. Against CEDGAN, T-GMSI achieves a 20% RMSE improvement on provided DEM data, requiring no fine-tuning. The ability of model on generalizing to large, unseen terrains underscores its transferability and potential applicability beyond topographic modeling. This research establishes T-GMSI as a state-of-the-art solution for spatial interpolation on sparse datasets and highlights its broader utility for other sparse data interpolation challenges.
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.
Fine-grained remote sensing image segmentation is essential for accurately identifying detailed objects in remote sensing images. Recently, vision transformer models (VTMs) pre-trained on large-scale datasets have demonstrated strong zero-shot generalization. However, directly applying them to specific tasks may lead to domain shift. We introduce a novel end-to-end learning paradigm combining knowledge guidance with domain refinement to enhance performance. We present two key components: the Feature Alignment Module (FAM) and the Feature Modulation Module (FMM). FAM aligns features from a CNN-based backbone with those from the pretrained VTM's encoder using channel transformation and spatial interpolation, and transfers knowledge via KL divergence and L2 normalization constraint. FMM further adapts the knowledge to the specific domain to address domain shift. We also introduce a fine-grained grass segmentation dataset and demonstrate, through experiments on two datasets, that our method achieves a significant improvement of 2.57 mIoU on the grass dataset and 3.73 mIoU on the cloud dataset. The results highlight the potential of combining knowledge transfer and domain adaptation to overcome domain-related challenges and data limitations. The project page is available at https://xavierjiezou.github.io/KTDA/.
In recent decades, statisticians have been increasingly encountering spatial data that exhibit non-Gaussian behaviors such as asymmetry and heavy-tailedness. As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate that the GSUN is a valid spatial process by showing its vanishing correlation in large distances and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over the conventional CNN-based architectures regarding stability and accuracy by means of a simulation study and application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey g-and-h processes, through the probability integral transform (PIT).
Radio map estimation (RME) involves spatial interpolation of radio measurements to predict metrics such as the received signal strength at locations where no measurements were collected. The most popular estimators nowadays project the measurement locations to a regular grid and complete the resulting measurement tensor with a convolutional deep neural network. Unfortunately, these approaches suffer from poor spatial resolution and require a great number of parameters. The first contribution of this paper addresses these limitations by means of an attention-based estimator named Spatial TransfOrmer for Radio Map estimation (STORM). This scheme not only outperforms the existing estimators, but also exhibits lower computational complexity, translation equivariance, rotation equivariance, and full spatial resolution. The second contribution is an extended transformer architecture that allows STORM to perform active sensing, by which the next measurement location is selected based on the previous measurements. This is particularly useful for minimization of drive tests (MDT) in cellular networks, where operators request user equipment to collect measurements. Finally, STORM is extensively validated by experiments with one ray-tracing and two real-measurement datasets.
Aggregated relative search frequencies offer a unique composite signal reflecting people's habits, concerns, interests, intents, and general information needs, which are not found in other readily available datasets. Temporal search trends have been successfully used in time series modeling across a variety of domains such as infectious diseases, unemployment rates, and retail sales. However, most existing applications require curating specialized datasets of individual keywords, queries, or query clusters, and the search data need to be temporally aligned with the outcome variable of interest. We propose a novel approach for generating an aggregated and anonymized representation of search interest as foundation features at the community level for geospatial modeling. We benchmark these features using spatial datasets across multiple domains. In zip codes with a population greater than 3000 that cover over 95% of the contiguous US population, our models for predicting missing values in a 20% set of holdout counties achieve an average $R^2$ score of 0.74 across 21 health variables, and 0.80 across 6 demographic and environmental variables. Our results demonstrate that these search features can be used for spatial predictions without strict temporal alignment, and that the resulting models outperform spatial interpolation and state of the art methods using satellite imagery features.
This note presents an approach for estimating the spatial distribution of static properties in reservoir modeling using a nearest-neighbor neural network. The method leverages the strengths of neural networks in approximating complex, non-linear functions, particularly for tasks involving spatial interpolation. It incorporates a nearest-neighbor algorithm to capture local spatial relationships between data points and introduces randomization to quantify the uncertainty inherent in the interpolation process. This approach addresses the limitations of traditional geostatistical methods, such as Inverse Distance Weighting (IDW) and Kriging, which often fail to model the complex non-linear dependencies in reservoir data. By integrating spatial proximity and uncertainty quantification, the proposed method can improve the accuracy of static property predictions like porosity and permeability.
Climate resilience across sectors varies significantly in low-income countries (LICs), with agriculture being the most vulnerable to climate change. Existing studies typically focus on individual countries, offering limited insights into broader cross-country patterns of adaptation and vulnerability. This paper addresses these gaps by introducing a framework for cross-country comparative analysis of sectoral climate resilience using meta-analysis and cross-country panel data techniques. The study identifies shared vulnerabilities and adaptation strategies across LICs, enabling more effective policy design. Additionally, a novel localized climate-agriculture mapping technique is developed, integrating sparse agricultural data with high-resolution satellite imagery to generate fine-grained maps of agricultural productivity under climate stress. Spatial interpolation methods, such as kriging, are used to address data gaps, providing detailed insights into regional agricultural productivity and resilience. The findings offer policymakers tools to prioritize climate adaptation efforts and optimize resource allocation both regionally and nationally.
Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data sets are typically limited to the spatial coordinates of the scattered observation locations. In this paper, we propose a hybrid framework that integrates data-driven spatial dependency feature extraction with rule-assisted spatial dependency function mapping to augment domain knowledge. We demonstrate the superior performance of our framework in two comparative application scenarios, highlighting its ability to capture more localized spatial features in the reconstructed distribution fields. Furthermore, we underscore its potential to enhance nonlinear estimation capabilities through the application of transformed fuzzy rules and to quantify the inherent uncertainties associated with the observation data sets. Our framework introduces an innovative approach to spatial information estimation by synergistically combining observational data with rule-assisted domain knowledge.
Evaluating house prices is crucial for various stakeholders, including homeowners, investors, and policymakers. However, traditional spatial interpolation methods have limitations in capturing the complex spatial relationships that affect property values. To address these challenges, we have developed a new method called Multi-Head Gated Attention for spatial interpolation. Our approach builds upon attention-based interpolation models and incorporates multiple attention heads and gating mechanisms to capture spatial dependencies and contextual information better. Importantly, our model produces embeddings that reduce the dimensionality of the data, enabling simpler models like linear regression to outperform complex ensembling models. We conducted extensive experiments to compare our model with baseline methods and the original attention-based interpolation model. The results show a significant improvement in the accuracy of house price predictions, validating the effectiveness of our approach. This research advances the field of spatial interpolation and provides a robust tool for more precise house price evaluation. Our GitHub repository.contains the data and code for all datasets, which are available for researchers and practitioners interested in replicating or building upon our work.
Conditional diffusion models can create unseen images in various settings, aiding image interpolation. Interpolation in latent spaces is well-studied, but interpolation with specific conditions like text or poses is less understood. Simple approaches, such as linear interpolation in the space of conditions, often result in images that lack consistency, smoothness, and fidelity. To that end, we introduce a novel training-free technique named Attention Interpolation via Diffusion (AID). Our key contributions include 1) proposing an inner/outer interpolated attention layer; 2) fusing the interpolated attention with self-attention to boost fidelity; and 3) applying beta distribution to selection to increase smoothness. We also present a variant, Prompt-guided Attention Interpolation via Diffusion (PAID), that considers interpolation as a condition-dependent generative process. This method enables the creation of new images with greater consistency, smoothness, and efficiency, and offers control over the exact path of interpolation. Our approach demonstrates effectiveness for conceptual and spatial interpolation. Code and demo are available at https://github.com/QY-H00/attention-interpolation-diffusion.
Predictions in the form of probability distributions are crucial for effective decision-making. Quantile regression enables such predictions within spatial prediction settings that aim to create improved precipitation datasets by merging remote sensing and gauge data. However, ensemble learning of quantile regression algorithms remains unexplored in this context and, at the same time, it has not been substantially developed so far in the broader machine learning research landscape. Here, we introduce nine quantile-based ensemble learners and address the afore-mentioned gap in precipitation dataset creation by presenting the first application of these learners to large precipitation datasets. We employed a novel feature engineering strategy, reducing predictors to distance-weighted satellite precipitation at relevant locations, combined with location elevation. Our ensemble learners include six ensemble learning and three simple methods (mean, median, best combiner), combining six individual algorithms: quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM), and quantile regression neural networks (QRNN). These algorithms serve as both base learners and combiners within different ensemble learning methods. We evaluated performance against a reference method (QR) using quantile scoring functions in a large dataset comprising 15 years of monthly gauge-measured and satellite precipitation in the contiguous United States (CONUS). Ensemble learning with QR and QRNN yielded the best results across quantile levels ranging from 0.025 to 0.975, outperforming the reference method by 3.91% to 8.95%. This demonstrates the potential of ensemble learning to improve probabilistic spatial predictions.
This study presents a data-driven spatial interpolation algorithm based on physics-informed graph neural networks used to develop national temperature-at-depth maps for the conterminous United States. The model was trained to approximately satisfy the three-dimensional heat conduction law by simultaneously predicting subsurface temperature, surface heat flow, and rock thermal conductivity. In addition to bottomhole temperature measurements, we incorporated other physical quantities as model inputs, such as depth, geographic coordinates, elevation, sediment thickness, magnetic anomaly, gravity anomaly, gamma-ray flux of radioactive elements, seismicity, and electric conductivity. We constructed surface heat flow, and temperature and thermal conductivity predictions for depths of 0-7 km at an interval of 1 km with spatial resolution of 18 km$^2$ per grid cell. Our model showed superior temperature, surface heat flow and thermal conductivity mean absolute errors of 4.8{\deg} C, 5.817 mW/m$^2$ and 0.022 W/(C-m)$, respectively. The predictions were visualized in two-dimensional spatial maps across the modeled depths. This thorough modeling of the Earth's thermal processes is crucial to understanding subsurface phenomena and exploiting natural underground resources.
Head-related transfer functions (HRTFs) are important for immersive audio, and their spatial interpolation has been studied to upsample finite measurements. Recently, neural fields (NFs) which map from sound source direction to HRTF have gained attention. Existing NF-based methods focused on estimating the magnitude of the HRTF from a given sound source direction, and the magnitude is converted to a finite impulse response (FIR) filter. We propose the neural infinite impulse response filter field (NIIRF) method that instead estimates the coefficients of cascaded IIR filters. IIR filters mimic the modal nature of HRTFs, thus needing fewer coefficients to approximate them well compared to FIR filters. We find that our method can match the performance of existing NF-based methods on multiple datasets, even outperforming them when measurements are sparse. We also explore approaches to personalize the NF to a subject and experimentally find low-rank adaptation to be effective.