Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem. Although surrogate models are generally employed to improve efficiency, the approach remains computationally prohibitive in high-dimensional settings. This paper proposes a novel RBDO framework based on a stochastic simulator viewpoint, in which the deterministic limit-state function and the uncertainty in the model inputs are combined into a unified stochastic representation. Under this formulation, the system response conditioned on a given design is modeled directly through its output distribution, rather than through an explicit limit-state function. Stochastic emulators are constructed in the design space to approximate the conditional response distribution, enabling the semi-analytical evaluation of failure probabilities or associated quantiles without resorting to Monte Carlo simulation. Two classes of stochastic emulators are investigated, namely generalized lambda models and stochastic polynomial chaos expansions. Both approaches provide a deterministic mapping between design variables and reliability constraints, which breaks the classical double-loop structure of RBDO and allows the use of standard deterministic optimization algorithms. The performance of the proposed approach is evaluated on a set of benchmark problems with dimensionality ranging from low to very high, including a case with stochastic excitation. The results are compared against a Kriging-based approach formulated in the full input space. The proposed method yields substantial computational gains, particularly in high-dimensional settings. While its efficiency is comparable to Kriging for low-dimensional problems, it significantly outperforms Kriging as the dimensionality increases.

Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in the training phase, which often are not available, and thus rely on synthetic data. Here, we present a reconstruction method that generates dense fields from sparse measurements, without assuming availability of the spatial statistics, nor of examples of the dense fields. This is made possible through the introduction of an automatically differentiable numerical simulator into the training phase of the method. The method is shown to have superior results over statistical and neural network based methods on a set of three standard problems from fluid mechanics.

The reliability of routine health data in low and middle-income countries (LMICs) is often constrained by reporting delays and incomplete coverage, necessitating the exploration of novel data sources and analytics. Geospatial Foundation Models (GeoFMs) offer a promising avenue by synthesizing diverse spatial, temporal, and behavioral data into mathematical embeddings that can be efficiently used for downstream prediction tasks. This study evaluated the predictive performance of three GeoFM embedding sources - Google Population Dynamics Foundation Model (PDFM), Google AlphaEarth (derived from satellite imagery), and mobile phone call detail records (CDR) - for modeling 15 routine health programmatic outputs in Malawi, and compared their utility to traditional geospatial interpolation methods. We used XGBoost models on data from 552 health catchment areas (January 2021-May 2023), assessing performance with R2, and using an 80/20 training and test data split with 5-fold cross-validation used in training. While predictive performance was mixed, the embedding-based approaches improved upon baseline geostatistical methods in 13 of 15 (87%) indicators tested. A Multi-GeoFM model integrating all three embedding sources produced the most robust predictions, achieving average 5-fold cross validated R2 values for indicators like population density (0.63), new HIV cases (0.57), and child vaccinations (0.47) and test set R2 of 0.64, 0.68, and 0.55, respectively. Prediction was poor for prediction targets with low primary data availability, such as TB and malnutrition cases. These results demonstrate that GeoFM embeddings imbue a modest predictive improvement for select health and demographic outcomes in an LMIC context. We conclude that the integration of multiple GeoFM sources is an efficient and valuable tool for supplementing and strengthening constrained routine health information systems.

Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the nonstationary characteristics of geographic variables. A common solution is trend surface modeling (e.g., Regression Kriging, RK), which relies on external explanatory variables to model the trend and then applies geostatistical interpolation to the residuals. However, this approach requires high-quality and readily available explanatory variables, which are often lacking in many spatial interpolation scenarios -- such as estimating heavy metal concentrations underground. This study proposes a Feature-Free Regression Kriging (FFRK) method, which automatically extracts geospatial features -- including local dependence, local heterogeneity, and geosimilarity -- to construct a regression-based trend surface without requiring external explanatory variables. We conducted experiments on the spatial distribution prediction of three heavy metals in a mining area in Australia. In comparison with 17 classical interpolation methods, the results indicate that FFRK, which does not incorporate any explanatory variables and relies solely on extracted geospatial features, consistently outperforms both conventional Kriging techniques and machine learning models that depend on explanatory variables. This approach effectively addresses spatial nonstationarity while reducing the cost of acquiring explanatory variables, improving both prediction accuracy and generalization ability. This finding suggests that an accurate characterization of geospatial features based on domain knowledge can significantly enhance spatial prediction performance -- potentially yielding greater improvements than merely adopting more advanced statistical models.

In this study, we investigate for the first time the low-rank properties of a tensorized large-scale spatio-temporal dynamic atmospheric variable. We focus on the Sentinel-5P tropospheric NO2 product (S5P-TN) over a four-year period in an area that encompasses the contiguous United States (CONUS). Here, it is demonstrated that a low-rank approximation of such a dynamic variable is feasible. We apply the low-rank properties of the S5P-TN data to inpaint gaps in the Sentinel-5P product by adopting a low-rank tensor model (LRTM) based on the CANDECOMP / PARAFAC (CP) decomposition and alternating least squares (ALS). Furthermore, we evaluate the LRTM's results by comparing them with spatial interpolation using geostatistics, and conduct a comprehensive spatial statistical and temporal analysis of the S5P-TN product. The results of this study demonstrated that the tensor completion successfully reconstructs the missing values in the S5P-TN product, particularly in the presence of extended cloud obscuration, predicting outliers and identifying hotspots, when the data is tensorized over extended spatial and temporal scales.

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.

Accurate precipitation estimates at individual locations are crucial for weather forecasting and spatial analysis. This study presents a paradigm shift by leveraging Deep Neural Networks (DNNs) to surpass traditional methods like Kriging for station-specific precipitation approximation. We propose two innovative NN architectures: one utilizing precipitation, elevation, and location, and another incorporating additional meteorological parameters like humidity, temperature, and wind speed. Trained on a vast dataset (1980-2019), these models outperform Kriging across various evaluation metrics (correlation coefficient, root mean square error, bias, and skill score) on a five-year validation set. This compelling evidence demonstrates the transformative power of deep learning for spatial prediction, offering a robust and precise alternative for station-specific precipitation estimation.

Per and polyfluoroalkyl substances (PFAS), chemicals found in products like non-stick cookware, are unfortunately persistent environmental pollutants with severe health risks. Accurately mapping PFAS contamination is crucial for guiding targeted remediation efforts and protecting public and environmental health, yet detection across large regions remains challenging due to the cost of testing and the difficulty of simulating their spread. In this work, we introduce FOCUS, a geospatial deep learning framework with a label noise-aware loss function, to predict PFAS contamination in surface water over large regions. By integrating hydrological flow data, land cover information, and proximity to known PFAS sources, our approach leverages both spatial and environmental context to improve prediction accuracy. We evaluate the performance of our approach through extensive ablation studies and comparative analyses against baselines like sparse segmentation, as well as existing scientific methods, including Kriging and pollutant transport simulations. Results highlight our framework's potential for scalable PFAS monitoring.

Kriging aims at estimating the attributes of unsampled geo-locations from observations in the spatial vicinity or physical connections, which helps mitigate skewed monitoring caused by under-deployed sensors. Existing works assume that neighbors' information offers the basis for estimating the attributes of the unobserved target while ignoring non-neighbors. However, non-neighbors could also offer constructive information, and neighbors could also be misleading. To this end, we propose ``Contrastive-Prototypical'' self-supervised learning for Kriging (KCP) to refine valuable information from neighbors and recycle the one from non-neighbors. As a pre-trained paradigm, we conduct the Kriging task from a new perspective of representation: we aim to first learn robust and general representations and then recover attributes from representations. A neighboring contrastive module is designed that coarsely learns the representations by narrowing the representation distance between the target and its neighbors while pushing away the non-neighbors. In parallel, a prototypical module is introduced to identify similar representations via exchanged prediction, thus refining the misleading neighbors and recycling the useful non-neighbors from the neighboring contrast component. As a result, not all the neighbors and some of the non-neighbors will be used to infer the target. To encourage the two modules above to learn general and robust representations, we design an adaptive augmentation module that incorporates data-driven attribute augmentation and centrality-based topology augmentation over the spatiotemporal Kriging graph data. Extensive experiments on real-world datasets demonstrate the superior performance of KCP compared to its peers with 6% improvements and exceptional transferability and robustness. The code is available at https://github.com/bonaldli/KCP

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.