Kernel Density Research Articles

Co-benefits and influencing factors exploration of air pollution and carbon reduction in China: Based on marginal abatement costs

This study addresses the pressing need for cost-effective emission reduction strategies that maximize co-benefits in terms of air pollution and carbon emissions. Our research contributes to the literature by accurately measuring these co-benefits, thereby facilitating their prompt realization in different regions. We employ an input-output framework that integrates carbon emissions and air pollution, allowing us to calculate marginal abatement costs using the shadow price of undesired output. Through this approach, we quantify the co-benefits and analyze the factors influencing them at both spatiotemporal and factor levels using spatial kernel density and geographical detectors. Our findings reveal several key insights: (1) under joint emission reduction efforts, we observe average annual reduction rates of 6.46% for marginal pollution and 6.10% for carbon reduction costs. Importantly, we document an increase in co-benefits from 0.50 to 0.86, characterized by an initial fluctuation followed by a linear increase. (2) the marginal cost difference for carbon emission and pollution reduction in western China was 179.45 and 155.08 respectively, compared to 321.51 and 124.70 in the Northeast, highlighting the crucial role of regional differences in shaping co-benefit outcomes. (3) we identify a negative spatial spillover effect between provinces, which diminishes over time, leading to heterogeneous effects when local provincial co-benefits exceed a threshold of 0.9. (4) during the adjustment period, we find that the industrial structure exerts significant single and interactive effects on co-benefits. Additionally, we highlight the critical role of environmental governance investment and government intervention as drivers of co-benefits in the current era. By offering the quantification of co-benefits under the marginal abatement costs, our study provides valuable scientific insights for planning and implementing effective synergy strategies.

Effects of plant taxonomic position on soil nematode communities in Antarctica.

Antarctica terrestrial ecosystems are facing the most threats from global climate change, which is altering plant composition greatly. These transformations may cause major reshuffling of soil community composition, including functional traits and diversity, and therefore affect ecosystem processes in Antarctica. We used high-throughput sequencing analysis to investigate soil nematodes under 3 dominant plant functional groups (lichens, mosses, and vascular plants) and bare ground in the Antarctic region. We calculated functional diversity of nematodes based on their diet, life histories, and body mass with kernel density n-dimensional hypervolumes. We also calculated taxonomic and functional beta diversity of the nematode communities based on Jaccard dissimilarity. The presence of plants had no significant effect on the taxonomic richness of nematodes but significantly increased nematode functional richness. The presence of plants also significantly decreased taxonomic beta diversity (homogenization). Only mosses and vascular plants decreased nematode functional beta diversity, which was mostly due to a decreased effect of the richness difference component. The presence of plants also increased the effect of deterministic processes potentially because environmental filtering created conditions favorable to nematodes at low trophic levels with short life histories and small body size. Increasing plant cover in the Antarctic due to climate change may lead to increased diversity of nematode species that can use the scarce resources and nematode taxonomic and functional homogenization. In a future under climate change, community restructuring in the region is possible.

How territoriality and sociality influence the habitat selection and movements of a large carnivore.

While territoriality is one of the key mechanisms influencing carnivore space use, most studies quantify resource selection and movement in the absence of conspecific influence or territorial structure. Our analysis incorporated social information in a resource selection framework to investigate mechanisms of territoriality and intra-specific competition on the habitat selection of a large, social carnivore. We fit integrated step selection functions to 3-h GPS data from 12 collared African wild dog packs in the Okavango Delta and estimated selection coefficients using a conditional Poisson likelihood with random effects. Packs selected for their neighbors' 30-day boundary (defined as their 95% kernel density estimate) and for their own 90-day core (defined as their 50% kernel density estimate). Neighbors' 30-day boundary had a greater influence on resource selection than any habitat feature. Habitat selection differed when they were within versus beyond their neighbors' 30-day boundary. Pack size, pack tenure, pup presence, and seasonality all mediated how packs responded to neighbors' space use, and seasonal dynamics altered the strength of residency. While newly-formed packs and packs with pups avoided their neighbors' boundary, older packs and those without pups selected for it. Packs also selected for the boundary of larger neighboring packs more strongly than that of smaller ones. Social structure within packs has implications for how they interact with conspecifics, and therefore how they are distributed across the landscape. Future research should continue to investigate how territorial processes are mediated by social dynamics and, in turn, how territorial structure mediates resource selection and movement. These results could inform the development of a human-wildlife conflict (HWC) mitigation tool by co-opting the mechanisms of conspecific interactions to manage space use of endangered carnivores.

A Lithium-Ion Battery Degradation Prediction Model With Uncertainty Quantification for Its Predictive Maintenance

Battery degradation modeling in the presence of uncertainty is a key but challenging issue in the applications of battery predictive maintenance. This paper develops a capacity prediction model with uncertainty quantification for lithium-ion batteries and proposes a dynamic maintenance strategy which can help to make an optimized decision at each battery cycle stage. To be specific, after using the one-dimensional convolution neural network (1dCNN), deep representative features hidden in original measured signals are extracted. Then, the bi-directional long short-term memory (Bi-LSTM) is applied to estimate the battery capacities, while the quantile regression (QR) layer is embedded into the construction of the Bi-LSTM network to obtain the capacities for different quantiles. Next, the kernel density estimation (KDE) is utilized to derive the probability density of the predicted points at each battery cycle stage. Thus, the combination of 1dCNN, Bi-LSTM, QR and KDE, named 1dCNN-BiLSTMQR-KDE, forms an efficacious capacity prediction model with reliable uncertainty management. Finally, the costs of different decisions at each battery cycle stage are evaluated, and the decision with the lower cost will be chosen. The whole proposition is verified on battery degradation datasets from NASA, and the comparison with other methods show that the proposed method is competitive.

Particle filtering supported probability density estimation of mobility patterns

This paper presents a methodology that aims to enhance the accuracy of probability density estimation in mobility pattern analysis by integrating prior knowledge of system dynamics and contextual information into the particle filter algorithm. The quality of the data used for density estimation is often inadequate due to measurement noise, which significantly influences the distribution of the measurement data. Thus, it is crucial to augment the information content of the input data by incorporating additional sources of information beyond the measured position data. These other sources can include the dynamic model of movement and the spatial model of the environment, which influences motion patterns. To effectively combine the information provided by positional measurements with system and environment models, the particle filter algorithm is employed, which generates discrete probability distributions. By subjecting these discrete distributions to exploratory techniques, it becomes possible to extract more certain information compared to using raw measurement data alone. Consequently, this study proposes a methodology in which probability density estimation is not solely based on raw positional data but rather on probability-weighted samples generated through the particle filter. This approach yields more compact and precise modeling distributions. Specifically, the method is applied to process position measurement data using a nonparametric density estimator known as kernel density estimation. The proposed methodology is thoroughly tested and validated using information-theoretic and probability metrics. The applicability of the methodology is demonstrated through a practical example of mobility pattern analysis based on forklift data in a warehouse environment.

Rural revitalization in China: Measurement indicators, regional differences and dynamic evolution

It is crucial to scientifically assess China's rural revitalization and grasp its evolution laws. This paper constructs an indicator system to measure the level of rural revitalization in China from 2011 to 2021 using the entropy weight method. Then, we explore the spatial and temporal divergence and dynamic evolutionary characteristics of rural revitalization using the Dagum Gini coefficient and Kernel density. We found that the level of rural revitalization in China is low but fluctuating and increasing. Regionally, eastern China scores higher than central, western and northeastern China. In terms of dimensions, ecological livability scores are higher than prosperous industry, effective governance, affluent living and civilized countryside in that order. The regional differences in the level of rural revitalization are mainly reflected between regions, especially between eastern and western China, but the gap between regions is narrowing year by year. And the results of the Kernel density show that the level of rural revitalization in China shows a slow and balanced growth, but the eastern China shows a polarization growth. These findings can provide a comprehensive and objective outline of the advantages and shortcomings of rural revitalization development in China, and provide a policy reference for the comprehensive and stable promotion of rural revitalization construction.

Spatial-temporal characteristics analysis and ecological environment quality evaluation of forest health care bases in Yunnan, Guizhou and Sichuan provinces

As the forest health care in China is still in the early stage of development, the construction standards of forest health care base are not unified yet, resulting in large differences in the evaluation criterion for the ecological environment of forest health care bases. So, it is urgent to develop a new forest health care ecological environment quality assessment method. Yunnan, Guizhou and Sichuan provinces of China were selected as the study area, the previous 6 batches of 165 national forest health care pilot construction bases were selected as the main data source. This study explored the spatial and temporal distribution characteristics of forest health care bases in the study area using standard deviation ellipses, kernel density estimation method and cold and hot spot analysis. Furthermore, this study evaluated the ecological environment quality of the forest health care bases with a new ecological environment quality evaluation index model, which assembled Fraction Vegetation Coverage(FVC), Wetness(WET), Evapotranspiration(ET), Land Surface Temperature(LST) and Normalized Difference Bare Soil Index(NDBSI). The results are as follows: (1) the forest health bases in the study area are mainly located by the east of the Hu Line with a northeast-southwest distribution direction characteristics, and gradually expanded into a shape of "high in the east and low in the west, multi-point development". (2) the area with ecological environment quality in excellent, good and medium grade accounts for about 87.73% in the study area, indicating that most of the study area is suitable for the construction of forest health care base. These results can provide a practical guidance for the further rational layout and balanced development of forest health care bases in the study area.

Interpretable Machine Learning for Finding Intermediate-mass Black Holes

Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine-learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to simulate GCs realistically, the simulation physics or initial conditions may fail to reflect reality fully. Therefore our training data may be biased, leading to a failure in generalization to observational data. Both the first issue—explainability/interpretability—and the second—out of distribution generalization and fairness—are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an Extreme Gradient Boosting (XGBoost) classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost, and a global rule from CORELS.

INTEGRATION NEEDS AND CHALLENGES FOR GREEN AND SMART TRANSFORMATION OF PORT INDUSTRY BASED ON MULTI-SOURCE DATA

This research explores the integration needs and challenges for achieving green and smart transformation in the port industry, leveraging multi-source data and geographic information technology. The study utilizes comprehensive data, including information from the National Enterprise Credit Information Publicity System, the National Catalogue Service for Geographic Information, and road network maps of Jiangsu Province in China. Geographical analysis methods, such as weighted kernel density estimation and standard deviation ellipse analysis, are employed to identify spatial distribution patterns and changes in the port and shipping service industry. The results indicate a spatial distribution pattern with weak expansion from the center, along the "northwest-southeast" direction. Challenges such as decentralized management and competition for interests hinder port integration for sustainable development. By understanding the spatial dynamics, policymakers can make informed decisions for a greener, smarter, and more efficient port sector.

Graph Convolutional Network-Enhanced Model for Screening Persistent, Mobile, and Toxic and Very Persistent and Very Mobile Substances.

The global management for persistent, mobile, and toxic (PMT) and very persistent and very mobile (vPvM) substances has been further strengthened with the rapid increase of emerging contaminants. The development of a ready-to-use and publicly available tool for the high-throughput screening of PMT/vPvM substances is thus urgently needed. However, the current model building with the coupling of conventional algorithms, small-scale data set, and simplistic features hinders the development of a robust model for screening PMT/vPvM with wide application domains. Here, we construct a graph convolutional network (GCN)-enhanced model with feature fusion of a molecular graph and molecular descriptors to effectively utilize the significant correlation between critical descriptors and PMT/vPvM substances. The model is built with 213,084 substances following the latest PMT classification criteria. The application domains of the GCN-enhanced model assessed by kernel density estimation demonstrate the high suitability for high-throughput screening PMT/vPvM substances with both a high accuracy rate (86.6%) and a low false-negative rate (6.8%). An online server named PMT/vPvM profiler is further developed with a user-friendly web interface (http://www.pmt.zj.cn/). Our study facilitates a more efficient evaluation of PMT/vPvM substances with a globally accessible screening platform.

Spatial distribution and influencing factors of rural tourism: A case study of Henan Province

Rural tourism is a powerful way to revitalize the countryside, and its spatial pattern is crucial for sustainable development. This paper analyzes the spatial distribution of rural tourism characteristic villages in Henan Province by taking 723 villages as the research object and using the nearest neighbor index, kernel density analysis, and spatial autocorrelation. It investigates the influencing factors utilizing the optimal parameters-based geographical detector (OPGD) model. The results show that, firstly, the overall spatial distribution of the rural tourism characteristic villages in Henan Province is characterized by aggregation and unbalanced distribution, and the overall spatial distribution density demonstrates the aggregation characteristics of “four cores and one belt”. Secondly, the rural tourism characteristic villages can be divided into four primary categories, agricultural industry, rural culture, and featured villages and towns. The spatial distributions of the four main categories are all clustered. Thirdly, the primary factors affecting the differences in the spatial distribution of the rural tourism characteristic villages are the topographic features, economic development level, tourism market potential, traffic capacity, and relevant policies, among which the critical factor is the number of A-class scenic spots in the tourism market potential. To promote the optimisation of the spatial pattern of rural tourism, it is necessary to strengthen resource integration. Furthermore, it is important to conduct in-depth exploration of more factors in order to provide comprehensive guidance for the sustainable development of rural tourism.

Landslide susceptibility prediction and mapping in Loess Plateau based on different machine learning algorithms by hybrid factors screening: Case study of Xunyi County, Shaanxi Province, China

Machine learning models are widely used for landslide susceptibility prediction (LSP). To better develop a landslide susceptibility prediction model for the Loess Plateau, this study compared different machine-learning models (Logistic regression (LR), support vector machines (SVM), random forests (RF), Naïve Bayes (NB), and multilayer perceptron (MLP)). Using Xunyi County, China as the study area, 1096 landslides were collected and divided into a training set (70%) and a test set (30%). Significant influencing factors were selected from 20 landslide factors using GeoDetector. The relationships between these factors and landslides were determined by normalized frequency ratios. Five trained machine learning models calculated landslide susceptibility indices and generated landslide susceptibility maps. Additionally, the accuracy (ACC), precision (PRE), recall (REC), F1 score, AUC values, LSI distribution characteristics, and overlay analysis of historical landslides with LSM were used to evaluate the performance of the models. The results show that the LSP results of the five models are generally reasonable. The results further indicated that the use of GeoDetector was able to filter out the main factors of eolian landslides, improving the predictive performance of the model and obtaining better LSMs. The RF model had the best overall performance, followed by the SVM, and the MLP model created LSM high susceptibility zones that could contain the highest number of historical landslides. The q-values of factor contributions indicate that elevation, NDVI, rainfall, POI kernel density, and RDLS are the main factors controlling landslides, which need to be paid attention to for landslide control in the Loess Plateau region. The results of this study can provide a reference for the follow-up study of landslide prevention and control, especially landslide susceptibility modeling in the Loess Plateau.

Spatial Pattern and Driving Mechanism of Urban Taxi Fares in China

Taxi fare is related to the daily life of residents. Reasonable taxi fare not only meets the travel demand of residents but also improves the income of drivers and promotes employment. The spatial variation of taxi fares exists between different regions and cities. Previous studies on taxi fares have been conducted mostly in individual cities, and there has been no study on the spatial differentiation pattern of taxi fares on a national scale. Taking 336 cities across China as the research object, a multiple linear regression model of taxi fares was established by demonstrating the spatial variation pattern of taxi fares, the global differentiation index, spatial autocorrelation analysis, and kernel density analysis, etc. The significance of the study is to explore the law of spatial differentiation of taxi fares in China and to provide a stenographic record of taxi fare adjustment. The results show that: (1) the spatial variation of taxi fares across the country is significant, with the starting taxi fare range being between RMB 4 and RMB 14. (2) The global differentiation index of taxi fares is large, with two low-low clusters and three high-high clusters appearing spatially, and the results of the kernel density analysis surface a dispersion distribution centered on provincial capitals. (3) The divergence pattern of taxis nationwide is influenced by several factors. A multiple linear regression model is selected to establish a multiple linear regression model of urban disposable income per capita, regional GDP, urbanization rate, and urban population density, which shows that urban disposable income per capita has the greatest influence on taxi fares. The model shows that urban disposable income per capita has the greatest influence on taxi fares, and the fare of a 5 km taxi ride is 6.07. Taxi fares have a clear pattern of spatial differentiation in China and are most affected by urban disposable income per capita. Through this study, we can gain a deeper understanding of the variation in taxi fares across the country and provide data and theoretical support for the rationality of taxi fare adjustments.

Spatial effects of green innovation and carbon emission reduction in China: Mediating role of infrastructure and informatization

Green innovation (GI) plays a vital role in mitigating urban carbon dioxide (CO2) emissions and fostering sustainable development in China. This study examines the impact of GI on CO2 emissions, underscoring its significance for environmental sustainability. The analysis of data from 253 Chinese cities from 2010 to 2020 shows a transition in GI from a “multipoint” sporadic pattern to a “clustered” aggregation, indicative of significant polarization. Concurrently, a converging trend in the CO2 emissions kernel density curve reflects the initial success of carbon reduction initiatives, demonstrating a notable “high in the north and low in the south” spatial disparity. Critically, the findings reveal that GI induces significant spatial spillover effects, reducing CO2 emissions not only locally but also in adjacent areas. The mediation analysis reveals that the level of infrastructure development acts as a masking factor, suggesting that despite infrastructure expansion potentially escalating CO2 emissions, alignment with GI principles steers its environmental impact towards a positive direction. Additionally, informatization's modest mediating role suggests that its enhancement, driven by GI, further mitigates CO2 emissions through improved resource efficiency. These insights highlight the importance of integrating GI into urban policy frameworks, emphasizing its role in environmental management and CO2 emission reduction.

Spatial information extraction of fishing grounds for light purse seine vessels in the Northwest Pacific Ocean based on AIS data

Ecological fishery management requires high-precision fishery information to support resource management and marine spatial planning. In this paper, the Automatic Identification System (AIS) was adopted to extract the spatial information on the fishing grounds of light purse seine vessels in the Northwest Pacific Ocean. The spatial distributions of fishing grounds mapped by the data mining, kernel density analysis and hotspot analysis methods were compared. The spatial similarity index was applied to determine the spatial consistency between the computed spatial information and fisheries resource information. Finally, the spatial information derived by the best method was used to investigate the characteristics of fishing activity. The results showed that: the speed of light purse seine vessels related to operations was lower than 1.6 knots. The spatial information extracted by the three methods was consistent with the catch data distribution, and the spatial similarity between the fishing effort and catch data was the highest. The spatial variation in fishing activity was similar to that in the chub mackerel migration route. AIS data could be used to provide high-resolution fishery information. Light purse seine fishing vessels typically operate and travel along the exclusive economic zone boundary, and increased attention must be given to fishing vessel operation supervision. A comprehensive supervision system can be employed to monitor the operations of fishing vessels more effectively. The results of this study can provide technical support for the management of fishing activities and conservation of marine resources in this region using AIS data.

Using Deep Learning to Detect Anomalies in On-Load Tap Changer Based on Vibro-Acoustic Signal Features

An On-Load Tap Changer (OLTC) that regulates transformer voltage is one of the most important and strategic components of a transformer. Detecting faults in this component at early stages is, therefore, crucial to prevent transformer outages. In recent years, Hydro Quebec initiated a project to monitor the OLTC’s condition in power transformers using vibro-acoustic signals. A data acquisition system has been installed on real OLTCs, which has been continuously measuring their generated vibration signal envelopes over the past few years. In this work, the multivariate deep autoencoder, a reconstruction-based method for unsupervised anomaly detection, is employed to analyze the vibration signal envelopes generated by the OLTC and detect abnormal behaviors. The model is trained using a dataset obtained from the normal operating conditions of the transformer to learn patterns. Subsequently, kernel density estimation (KDE), a nonparametric method, is used to fit the reconstruction errors (regarding normal data) obtained from the trained model and to calculate the anomaly scores, along with the static threshold. Finally, anomalies are detected using a deep autoencoder, KDE, and a dynamic threshold. It should be noted that the input variables responsible for anomalies are also identified based on the value of the reconstruction error and standard deviation. The proposed method is applied to six different real datasets to detect anomalies using two distinct approaches: individually on each dataset and by comparing all six datasets. The results indicate that the proposed method can detect anomalies at an early stage. Also, three alarms, including ignorable anomalies, long-term changes, and significant alterations, were introduced to quantify the OLTC’s condition.

“Characterization of residential proximity to sources of environmental carcinogens in clusters of Acute Lymphoblastic Leukemia in San Luis Potosi, Mexico”

BackgroundAcute Lymphoblastic Leukemia (ALL) is the most prevalent neoplasia in children and teenagers in Mexico. Although epidemiological data supports that children's residence close to emissions from vehicular traffic or industrial processes increases the risk of ALL; and the IARC states that benzene, PAHs, and PM 2.5 are well-known environmental carcinogens, there is a gap in linking these carcinogenic hazards with the sources and their distribution from scenario perspective. AimTo identify ALL clusters in the population under 19 years of age and characterize the environment at the neighborhood level by integrating information on sources of carcinogenic exposure using spatial analysis techniques in the Metropolitan Area of San Luis Potosi, Mexico. MethodsUsing the Kernel Density test, we designed an ecological study to identify ALL clusters from incident cases in the population under 19 years of age. A multicriteria analysis was conducted to characterize the risk at the community level from carcinogenic sources. A hierarchical cluster analysis was performed to characterize risk at the individual level based on carcinogenic source count within 1 km for each ALL case. ResultsEight clusters of carcinogenic sources were located within the five identified ALL clusters. The multicriteria analysis showed high-risk areas (by density of carcinogenic source) within ALL clusters. ConclusionsThis study has a limited source and amount of available data on ALL cases, so selection bias is present as well as the inability to rule out residual confounding factors, since covariates were not included. However, in this study, children living in environments with high vehicular density, gas stations, brick kilns, incinerators, commercial establishments burning biomass, or near industrial zones may be at higher risk for ALL.

The mode I fracture toughness and acoustic emission characteristics of hot dry rock under temperature effects

The application of liquid nitrogen fracturing technology exhibits promising potential in the exploitation of hot dry rock (HDR). Therefore, studying the variation in granite's fracture characteristics under rapid cooling with liquid nitrogen is highly significant. In this study, the mode I fracture characteristics and acoustic emission (AE) characteristics of thermally treated granite under liquid nitrogen cooling were investigated experimentally. The results indicate that as the temperature increases, both the natural cooling group and liquid nitrogen cooling group exhibit a gradual decrease in granite's fracture toughness, and the cooling effect of liquid nitrogen will further damage the granite. When heated from 25 °C to 600 °C, the natural cooling fracture toughness decreased from 1.089 MPa·m1/2 to 0.1631 MPa·m1/2, with a reduction of 85.0 %; the liquid nitrogen cooling fracture toughness decreased from 1.089 MPa·m1/2 to 0.1493 MPa·m1/2, with a reduction of 86.3 %. Additionally, both the peak load and fracture energy are reduced; intragranular fracture behavior is observed within the granite, resulting in a rougher fracture surface. The integration of a crack classification method based on the rise angle (RA) and average frequency (AF) of AE parameters with the kernel density estimation (KDE) method effectively validates the fracture mechanism of semi-circular bend (SCB) specimens. Meanwhile, based on the AE results during granite fracturing, a method is proposed to discriminate crack types using RA and AF thresholds.

Performance of T2-based PCA mix control chart with KDE control limit for monitoring variable and attribute characteristics

In this work, the mixed multivariate T2 control chart’s detailed performance evaluation based on PCA mix is explored. The control limit of the proposed control chart is calculated using the kernel density approach. Through simulation studies, the proposed chart’s performance is assessed in terms of its capacity to identify outliers and process shifts. When 30% more outliers are included in the data, the proposed chart provides a consistent accuracy rate for identifying mixed outliers. For the balanced percentage of attribute qualities, misdetection happens because of the high false alarm rate. For unbalanced attribute qualities and excessive proportions, the masking effect is the key issue. The proposed chart shows the improved performance for the shift in identifying the shift in the process.

Non‐uniform active learning for Gaussian process models with applications to trajectory informed aerodynamic databases

AbstractThe ability to non‐uniformly weight the input space is desirable for many applications, and has been explored for space‐filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, we apply non‐uniform sampling methods for the construction of aerodynamic databases. This paper combines non‐uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed‐form solution to a non‐uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.