We present a transfer-learning generative downscaling framework to reconstruct fine resolution satellite images from coarse scale inputs. Our approach combines a lightweight U-Net transfer encoder with a diffusion-based generative model. The simpler U-Net is first pretrained on a long time series of coarse resolution data to learn spatiotemporal representations; its encoder is then frozen and transferred to a larger downscaling model as physically meaningful latent features. Our application uses NASA's MERRA-2 reanalysis as the low resolution source domain (50 km) and the GEOS-5 Nature Run (G5NR) as the high resolution target (7 km). Our study area included a large area in Asia, which was made computationally tractable by splitting into two subregions and four seasons. We conducted domain similarity analysis using Wasserstein distances confirmed minimal distributional shift between MERRA-2 and G5NR, validating the safety of parameter frozen transfer. Across seasonal regional splits, our model achieved excellent performance (R2 = 0.65 to 0.94), outperforming comparison models including deterministic U-Nets, variational autoencoders, and prior transfer learning baselines. Out of data evaluations using semivariograms, ACF/PACF, and lag-based RMSE/R2 demonstrated that the predicted downscaled images preserved physically consistent spatial variability and temporal autocorrelation, enabling stable autoregressive reconstruction beyond the G5NR record. These results show that transfer enhanced diffusion models provide a robust and physically coherent solution for downscaling a long time series of coarse resolution images with limited training periods. This advancement has significant implications for improving environmental exposure assessment and long term environmental monitoring.

Accurate and robust image-based geo-localization at a global scale is challenging due to diverse environments, visually ambiguous scenes, and the lack of distinctive landmarks in many regions. While contrastive learning methods show promising performance by aligning features between street-view images and corresponding locations, they neglect the underlying spatial dependency in the geographic space. As a result, they fail to address the issue of false negatives -- image pairs that are both visually and geographically similar but labeled as negatives, and struggle to effectively distinguish hard negatives, which are visually similar but geographically distant. To address this issue, we propose a novel spatially regularized contrastive learning strategy that integrates a semivariogram, which is a geostatistical tool for modeling how spatial correlation changes with distance. We fit the semivariogram by relating the distance of images in feature space to their geographical distance, capturing the expected visual content in a spatial correlation. With the fitted semivariogram, we define the expected visual dissimilarity at a given spatial distance as reference to identify hard negatives and false negatives. We integrate this strategy into GeoCLIP and evaluate it on the OSV5M dataset, demonstrating that explicitly modeling spatial priors improves image-based geo-localization performance, particularly at finer granularity.

A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering algorithms overlook the rich correlation between feature similarity and metric distance, i.e., metric autocorrelation. The model-based variations of these clustering algorithms (e.g. TICC and STICC) achieve SOTA performance, yet suffer from computational instability and complexity by using a metric-constrained Expectation-Maximization procedure. In order to address these two problems, we propose a novel clustering algorithm, MC-GTA (Model-based Clustering via Goodness-of-fit Tests with Autocorrelations). Its objective is only composed of pairwise weighted sums of feature similarity terms (square Wasserstein-2 distance) and metric autocorrelation terms (a novel multivariate generalization of classic semivariogram). We show that MC-GTA is effectively minimizing the total hinge loss for intra-cluster observation pairs not passing goodness-of-fit tests, i.e., statistically not originating from the same distribution. Experiments on 1D/2D synthetic and real-world datasets demonstrate that MC-GTA successfully incorporates metric autocorrelation. It outperforms strong baselines by large margins (up to 14.3% in ARI and 32.1% in NMI) with faster and stabler optimization (>10x speedup).

Fusing abundant satellite data with sparse ground measurements constitutes a major challenge in climate modeling. To address this, we propose a strategy to augment the training dataset by introducing unlabeled satellite images paired with pseudo-labels generated through a spatial interpolation technique known as ordinary kriging, thereby making full use of the available satellite data resources. We show that the proposed data augmentation strategy helps enhance the performance of the state-of-the-art convolutional neural network-random forest (CNN-RF) model by a reasonable amount, resulting in a noteworthy improvement in spatial correlation and a reduction in prediction error.

As the role played by statistical and computational sciences in climate modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle the climate crisis. Indeed, being universal nonlinear fucntion approximation tools, Machine Learning algorithms are efficient in analysing and modelling spatially and temporally variable climate data. While Deep Learning models have proved to be able to capture spatial, temporal, and spatio-temporal dependencies through their automatic feature representation learning, the problem of the interpolation of continuous spatio-temporal fields measured on a set of irregular points in space is still under-investigated. To fill this gap, we introduce here a framework for spatio-temporal prediction of climate and environmental data using deep learning. Specifically, we show how spatio-temporal processes can be decomposed in terms of a sum of products of temporally referenced basis functions, and of stochastic spatial coefficients which can be spatially modelled and mapped on a regular grid, allowing the reconstruction of the complete spatio-temporal signal. Applications on two case studies based on simulated and real-world data will show the effectiveness of the proposed framework in modelling coherent spatio-temporal fields.