Ground Truth Dataset Research Articles

Enhancing Soil Texture and Bulk Density Mapping Using Soil Grids and Machine Learning: A Comparative Analysis with Observed Data

Digital soil mapping plays a crucial role in understanding soil variability and informing sustainable land management practices. This study focuses on the Kurdistan Region of Iraq (KRI), evaluating the accuracy of SoilGrids, a global-scale soil mapping initiative, and exploring the efficacy of machine learning algorithms in refining soil properties estimations. The aim of this research was to assess and represent the physical parameters of soils effectively by comparing ground truth soil sampling data with data obtained from SoilGrids regarding clay, silt, and sand fractions and bulk density. Comparative analyses were conducted between ground truth soil sampling data and SoilGrids predictions, revealing significant differences across soil mineral fractions including clay, silt, sand fractions, and bulk density. The results showed that the mean clay fraction in the ground truth dataset differed notably from SoilGrids estimation, with a Mean Absolute Deviation (MAD) of 124.0 g kg-1 and Root Mean Square Error (RMSE) of 152.5. However, the integration of machine learning algorithms, particularly the Extreme Gradient Boosting (XG Boost) algorithm, showed promising results in improving accuracy. The XG Boost algorithm exhibited a relatively low MAD of 97.9 g kg-1 for clay fractions, indicating a better approximation of observed values compared to SoilGrids. Significant percent improvements in RMSE and Mean Absolute Percentage Error (MAPE) values were observed across soil fractions and bulk density measurements, ranging from approximately 15% for clay to 35% for sand fractions and 20% for bulk density. These findings highlight the importance of integrating advanced mapping techniques and machine learning algorithms to enhance soil mapping methodologies. Moving forward, efforts to expand ground truth datasets through targeted soil sampling campaigns and develop international collaboration initiatives will be crucial for improving the accuracy and reliability of soil mapping products in the KRI. By incorporating advanced mapping approaches, we can better support sustainable land management practices and environmental conservation efforts in the region.

Seasonally flooded landscape connectivity and implications for fish in the Napo Moist Forest: A high-resolution mapping approach

The Amazon River Basin's fish diversity is shaped by its dynamic flood-pulse system, critical for hydrological and ecological connectivity. This study examines the Napo Moist Forest (NMF) ecoregion, mapping permanent and seasonally flooded areas from 2018 to 2021 using remote sensing and deep learning models. We aimed to map these areas at a high spatial resolution (10-m pixels) and analyse their role in maintaining lateral connectivity essential for fish diversity. Using synthetic aperture radar data from Sentinel-1 combined with deep learning algorithms, we produced high-accuracy flood maps to assess landscape connectivity between rivers and floodplains. Our methodology included creating a ground truth dataset with the Normalized Difference Water Index and integrating high-resolution optical data for model training, overcoming challenges of cloud coverage and dense vegetation. Our predictive model achieved high accuracy (mean pixel accuracy = 97 %) and consistently predicted 4801 km² of surface water, with only 3 % (130 km²) being seasonally flooded areas over four years. The Caquetá, Bajo Marañón, Napo, and Pastaza watersheds accounted for nearly 60 % of the flooded areas, highlighting their ecological importance. Connectivity analysis in three areas of interest within the NMF ecoregion revealed important seasonal and interannual fluctuations in hydrological connectivity due to changes in flooded patch characteristics. Reductions in the number and flooded patch area during low water seasons increased the distance between patches, leading to a disconnection between flooded areas, channels and rivers. Despite hydrological fluctuations, certain patches maintained consistent flooding, critical for lateral connectivity and sustaining aquatic biodiversity. These seasonally flooded areas act as connectors, influencing patch dynamics and connectivity with tributaries. Seasonal and interannual variations in hydrological connectivity are crucial for sustaining fish diversity. Conserving dynamic floodplains supports migratory fish life cycles and biodiversity. This study underscores the importance of high-resolution temporal and spatial data in conservation planning for aquatic ecosystems.

BoReMi: Bokeh-based jupyter-interface for registering spatio-molecular data to related microscopy images.

Spatio-molecular data and microscopy images provide complementary information, essential to study structure and function of spatially organised multicellular systems such as healthy or diseased tissues. However, aligning these two types of data can be challenging due to distortions and differences in resolution, orientation, and position. Manual registration is tedious but may be necessary for challenging samples as well as for the generation of ground-truth data sets that enable benchmarking of existing and emerging automated alignment tools. To make the process of manual registration more convenient, efficient, and integrated, we created BoReMi, a python-based, Jupyter-integrated, visual tool that offers all the relevant functionalities for aligning and registering spatio-molecular data and associated microscopy images. We showcase BoReMi's utility using publicly available data and images and make BoReMi as well as an interactive demo available on GitHub.

Remote sensing assessment of wildfire using high-resolution PlanetScope satellite observations: A case study on Co Tien Mountain, Nha Trang City, Vietnam

In this study, high spatial resolution (3 m) PlanetScope (PS) imagery was utilized to map burned areas caused by a wildfire occurring on January 10, 2024, on Co Tien Mountain in Nha Trang city, Khanh Hoa province, South Central Coast of Vietnam. A pre-fire image, acquired ten days earlier, on December 31, 2023, and a post-fire one, acquired nearly one month after, on February 04, 2024, were used to create pre- and post-fire Normalized Difference Vegetation Index (NDVI) maps of the study area, then the difference of NDVI (dNDVI). A threshold (T = 0.20), proposed by the author, was applied to the histogram of the dNDVI product to classify the study area into two clusters: burned pixels (dNDVI > T) and unburned pixels (dNDVI <= T). Classification results estimate that a total of 16.11 ha of grass, reeds, small shrubs and vegetation have been burned out during the wildfire. A field trip is required to map the burned areas using unmanned aerial vehicles (UAVs) for an accurate validation of results derived purely from PS satellite observations. Although lacking a ground truth dataset for validation is a significant limitation, the proposed approach remains beneficial for local managers and decision-makers. It enables the rapid assessment of damages caused by small wildfires and provides essential data for effective disaster management and recovery planning, particularly in remote areas.

Artificial Intelligence Tools in Pediatric Urology: A Comprehensive Review of Recent Advances.

Artificial intelligence (AI) is providing novel answers to long-standing clinical problems, and it is quickly changing pediatric urology. This thorough analysis focuses on current developments in AI technologies that improve pediatric urology diagnosis, treatment planning, and surgery results. Deep learning algorithms help detect problems with previously unheard-of precision in disorders including hydronephrosis, pyeloplasty, and vesicoureteral reflux, where AI-powered prediction models have demonstrated promising outcomes in boosting diagnostic accuracy. AI-enhanced image processing methods have significantly improved the quality and interpretation of medical images. Examples of these methods are deep-learning-based segmentation and contrast limited adaptive histogram equalization (CLAHE). These methods guarantee higher precision in the identification and classification of pediatric urological disorders, and AI-driven ground truth construction approaches aid in the standardization of and improvement in training data, resulting in more resilient and consistent segmentation models. AI is being used for surgical support as well. AI-assisted navigation devices help with difficult operations like pyeloplasty by decreasing complications and increasing surgical accuracy. AI also helps with long-term patient monitoring, predictive analytics, and customized treatment strategies, all of which improve results for younger patients. However, there are practical, ethical, and legal issues with AI integration in pediatric urology that need to be carefully navigated. To close knowledge gaps, more investigation is required, especially in the areas of AI-driven surgical methods and standardized ground truth datasets for pediatric radiologic image segmentation. In the end, AI has the potential to completely transform pediatric urology by enhancing patient care, increasing the effectiveness of treatments, and spurring more advancements in this exciting area.

Comparative analysis of saliency map algorithms in capturing visual priorities for building inspections

This study investigates the efficacy of saliency mapping algorithms in capturing the visual priorities of building inspectors for structural damage assessment. Our work established a ground truth dataset by implementing eye-tracking technology to capture the gaze patterns of building inspectors. Further, it enables a detailed evaluation of the saliency models’ ability to reflect experts' visual attention during inspection tasks. Our comparative analysis assesses the performance of three saliency models— EnDec, DeepGaze, and SALICON— against this ground truth data, using conventional saliency metrics such as Area under the Curve, Similarity, Normalized Scanpath Saliency, Correlation Coefficient, and Kullback-Leibler Divergence. Our findings reveal that while the SALICON model demonstrates a marginally better performance and highlights areas where these models fall short, particularly in accurately reflecting the critical visual properties of inspectors, this insight is crucial for advancing the field. By highlighting these limitations, we have drawn attention to the need for developing more specialized saliency models tailored to the unique demands of building inspection tasks. Thus, the study not only fulfills its objectives of comparative analysis but also contributes to the broader discourse on improving automated structural inspection systems. This study highlights the need to develop specialized computer vision models to address specific building inspection challenges. By identifying strengths and improvement areas, this research contributes valuable insights and highlights the potential and current limitations of applying computer vision techniques to real-world building inspection tasks.

Breast cancer characterization using region-based convolutional neural network with screening and diagnostic mammogram

Background: Detection and classification of microcalcifications in breast tissues is crucial for early breast cancer diagnosis and long-term treatment. Objective: This paper aims to propose a robust model capable of detection and classification of breast cancer calcifications in digital mammogram images using Deep Convolutional Neural Networks (DCNN). Materials and methods: An expert breast radiologist annotated the 3,265 clinical mammogram images to create a comprehensive ground truth dataset comprising 2,500 annotations for malignant and benign calcifications. This dataset was utilized to train our model, a two-stage detection system incorporating a Region-based Convolutional Neural Network (RCNN) with AlexNet and support vector machines to enhance the system’s robustness. The proposed model was compared to the one-stage detection, utilizing YOLOv4 combined with the Cross-Stage Partial Darknet53 (CSPDarknet53) architecture. A separate dataset of 504 mammogram images was explicitly set aside for model testing. The efficacy of the proposed model was evaluated based on key performance metrics, including precision, recall, F1 score, and mean average precision (mAP). Results: The results showed that the proposed RCNN-2 model could automatically identify and categorize calcifications as malignant or benign, outperforming the YOLOv4 models. The RCNN-2’s overall effectiveness, as evaluated by precision, recall, F1 score, and mean average precision (mAP), achieved scores of 0.82, 0.85, 0.83, and 0.74, respectively. Conclusion: The proposed RCNN-2 model demonstrates very effective detection and classification of calcification in mammogram images, especially in high-dense breast images. The performance of the proposed model was compared to that of YOLOv4, and it can be concluded that the proposed RCNN model yields outstanding performance. The model can be a helpful tool for radiologists.

DETECTION OF FAKE NEWS ON TWITTER USING MACHINE LEARNING: AN XGBOOST-BASED APPROACH WITH SENTIMENT AND SOURCE CHARACTERISTIC ANALYSIS

The spread of fake news on social media platforms is becoming an increasingly alarming problem with fake news becoming more deceptive and harder to detect. Twitter, in particular, poses a significant threat as fake news spreads faster than real news on the platform, enhancing misinformation and leading to serious consequences.This project presents a novel machine learning-based approach for detecting fake news tweets on Twitter using the TruthSeeker 2023 dataset from the University of New Brunswick. As the largest ground truth dataset for fake news detection on social media, it contains over 130,000 crowdsourced tweets, enabling the creation of a broader and more applicable model for real-world scenarios. The algorithm employed in this study leverages the properties of gradient-boosted decision tree models (XGBoost) to develop a novel method for classifying fake and real news tweets. The proposed model preprocesses the data by extracting additional features for each tweet, such as detailed sentiment analysis of both the tweet and the related news statement, as well as features pertaining to the author. These features are added to the tweets feature vector. The enhanced feature vectors are then fed into an XGBoost model with tuned hyperparameters determined through a grid search algorithm to perform binary classification. The additional extracted features increase the robustness of the model by highlighting key differentiating factors between real and fake tweets. The results of this study demonstrate the effectiveness of the proposed algorithm, achieving an accuracy of 0.9335 on over 13,000 unseen tweets.

Extensive co-regulation of neighboring genes complicates the use of eQTLs in target gene prioritization

Identifying causal genes underlying genome-wide association studies (GWAS) is a fundamental problem in human genetics. Although colocalisation with gene expression quantitative trait loci (eQTLs) is often used to prioritise GWAS target genes, systematic benchmarking has been limited due to unavailability of large ground truth datasets. Here, we re-analysed plasma protein QTL data from 3,301 individuals of the INTERVAL cohort together with 131 eQTL Catalogue datasets. Focusing on variants located within or close to the affected protein identified 793 proteins with at least one cis-pQTL where we could assume that the most likely causal gene was the gene coding for the protein. We then benchmarked the ability of cis-eQTLs to recover these causal genes by comparing three Bayesian colocalisation methods (coloc.susie, coloc.abf and CLPP) and five Mendelian randomisation (MR) approaches (three varieties of inverse-variance weighted MR, MR-RAPS, and MRLocus). We found that assigning fine-mapped pQTLs to their closest protein coding genes outperformed all colocalisation methods regarding both precision (71.9%) and recall (76.9%). Furthermore, the colocalisation method with the highest recall (coloc.susie - 46.3%) also had the lowest precision (45.1%). Combining evidence from multiple conditionally distinct colocalising QTLs with MR increased precision to 81%, but this was accompanied by a large reduction in recall to 7.1%. Furthermore, the choice of the MR method greatly affected performance, with the standard inverse-variance weighted MR often producing many false positives. Our results highlight that linking GWAS variants to target genes remains challenging with eQTL evidence alone, and prioritising novel targets requires triangulation of evidence from multiple sources.

Mapping of irrigated vineyard areas through the use of machine learning techniques and remote sensing

Effective and sustainable management of aquifers in regions with intensive groundwater use for irrigation requirements accurate mapping or irrigated areas to control water resource exploitation and plan rational water usage. This study proposes a cost-effective methodology based on satellite images to identify irrigated areas utilizing surface water and groundwater resources. The methodology integrates soil moisture estimations, environmental variables, and variables that affect to retention of water soil, that join a ground truth dataset, to estimate irrigated surface through a machine learning method during the irrigation period of 2021. Spectral data derived parameters and crop morphology, along with official data on agricultural parcels, were utilized to define vineyard irrigation areas at the plot scale within the Requena-Utiel aquifer in Eastern Spain. A machine learning classification technique was applied,yielding a remarkable precision of 91.8 % when compared to ground truth data.Discrepancies between the remote sensing-based irrigated area estimation and official data are highlighted. This study represents the most accurate plot-scale irrigation mapping of woody crops in the region to date.

Anisotropic DBSCAN for 3D SMLM Data Clustering.

Single-molecule localization microscopy (SMLM) advanced biological discoveries beyond the diffraction limit. Various implementations enable 3D SMLM to reconstruct volumetric cell images. Yet, the inherent anisotropic point spread function of optical microscopes often limits the localization precision in the axial direction compared to the lateral precision. Such localization anisotropy could also expand spherical cellular structures to ellipsoidal cellular structures. Structure identification, however, is often performed using DBSCAN cluster algorithms, considering an isotropic search volume. Here, we show that an anisotropic DBSCAN search volume identifies anisotropic clusters more reliably using simulated ground truth data sets. Given experimental localization precisions, we suggest optimized search parameters based on an expanded computational grid search and show an enhanced performance of anisotropic DBSCAN amidst variations in localization precision. We demonstrate the capability of anisotropic DBSCAN on experimental data and anticipate that the algorithm allows for a more rigorous identification of clusters in cells, considering the anisotropic localization precisions of astigmatism-based 3D SMLM.

Streak artefact removal in x-ray dark-field computed tomography using a convolutional neural network.

Computed tomography (CT) relies on the attenuation of x-rays, and is, hence, of limited use for weakly attenuating organs of the body, such as the lung. X-ray dark-field (DF) imaging is a recently developed technology that utilizes x-ray optical gratings to enable small-angle scattering as an alternative contrast mechanism. The DF signal provides structural information about the micromorphology of an object, complementary to the conventional attenuation signal. A first human-scale x-ray DF CT has been developed by our group. Despite specialized processing algorithms, reconstructed images remain affected by streaking artifacts, which often hinder image interpretation. In recent years, convolutional neural networks have gained popularity in the field of CT reconstruction, amongst others for streak artefactremoval. Reducing streak artifacts is essential for the optimization of image quality in DF CT, and artefact free images are a prerequisite for potential future clinical application. The purpose of this paper is to demonstrate the feasibility of CNN post-processing for artefact reduction in x-ray DF CT and how multi-rotation scans can serve as a pathway for trainingdata. We employed a supervised deep-learning approach using a three-dimensional dual-frame UNet in order to remove streak artifacts. Required training data were obtained from the experimental x-ray DF CT prototype at our institute. Two different operating modes were used to generate input and corresponding ground truth data sets. Clinically relevant scans at dose-compatible radiation levels were used as input data, and extended scans with substantially fewer artifacts were used as ground truth data. The latter is neither dose-, nor time-compatible and, therefore, unfeasible for clinical imaging ofpatients. The trained CNN was able to greatly reduce streak artifacts in DF CT images. The network was tested against images with entirely different, previously unseen image characteristics. In all cases, CNN processing substantially increased the image quality, which was quantitatively confirmed by increased image quality metrics. Fine details are preserved during processing, despite the output images appearing smoother than the ground truthimages. Our results showcase the potential of a neural network to reduce streak artifacts in x-ray DF CT. The image quality is successfully enhanced in dose-compatible x-ray DF CT, which plays an essential role for the adoption of x-ray DF CT into modern clinicalradiology.

Prediction of residential building occupancy using Machine learning with integrated sensor and survey Data: Insights from a living lab in Morocco

Building occupancy information is essential for effective energy management in buildings through the adoption of energy conservation and occupant-centric control strategies. These strategies endeavor to contribute to optimizing energy consumption while ensuring occupant comfort. This study focuses on advanced occupancy modeling techniques to enhance energy efficiency in residential buildings, utilizing various data-driven techniques. Various Machine Learning models, such as Random Forest, Bayesian Network, Decision Trees, Support Vector Machines, K-Nearest Neighbors, eXtreme Gradient Boosting, and Regularized Greedy Forest, have been evaluated for predicting and classifying building occupancy. Employing a living lab approach within a residential setting, the research evaluates model performance using two ground truth datasets: IoT sensor and survey data. Experimental tests use Accuracy and F1_score as evaluation criteria, demonstrating accuracy rates ranging from 70% to 95.96%. The results highlight the performance of these models in predicting residential occupancy, offering valuable insight into two approaches to occupancy modeling. The Random Forest model performs exceptionally well in capturing occupancy trends, while the Bayesian Network model, combined with expert knowledge, provides detailed predictions of occupancy types and zones. The research also addresses challenges related to data collection, including privacy concerns. It presents effective occupancy modeling strategies for residential energy management.

A Review Study on Outbreak Prediction of Covid19 By using Machine Learning

In December 2019, Wuhan City, China, discovered a new infectious disease, COVID-19. Over 70 million people have been infected and one million people have died as a result of COVID-19. Defeating such a deadly, infectious disease requires accurate models that predict COVID-19 outbreaks. Using prediction models, governments can plan budgets and facilities for fighting diseases, and take control measures to make better decisions and take control measures. For example, they can determine how many medicines and medical equipment to manufacture or import, as well as how many medical personnel are needed to fight the disease. The COVID-19 outbreak has subsequently been predicted in several countries and continents using regression and classification models. A recent study that incorporated statistical and machine learning techniques was reviewed to predict COVID-19 outbreaks in the future. Ground truth datasets are used, their characteristics are investigated, models are developed, predictor variables are identified, statistical and machine learning methods are applied, performance metrics are calculated, and finally comparisons are made. By applying machine learning methods, the survey results indicate that we can make predictions about whether a patient will become infected with COVID-19, how outbreak trends will develop, and which age groups will be affected the most

Image2Flow: A proof-of-concept hybrid image and graph convolutional neural network for rapid patient-specific pulmonary artery segmentation and CFD flow field calculation from 3D cardiac MRI data.

Computational fluid dynamics (CFD) can be used for non-invasive evaluation of hemodynamics. However, its routine use is limited by labor-intensive manual segmentation, CFD mesh creation, and time-consuming simulation. This study aims to train a deep learning model to both generate patient-specific volume-meshes of the pulmonary artery from 3D cardiac MRI data and directly estimate CFD flow fields. This proof-of-concept study used 135 3D cardiac MRIs from both a public and private dataset. The pulmonary arteries in the MRIs were manually segmented and converted into volume-meshes. CFD simulations were performed on ground truth meshes and interpolated onto point-point correspondent meshes to create the ground truth dataset. The dataset was split 110/10/15 for training, validation, and testing. Image2Flow, a hybrid image and graph convolutional neural network, was trained to transform a pulmonary artery template to patient-specific anatomy and CFD values, taking a specific inlet velocity as an additional input. Image2Flow was evaluated in terms of segmentation, and the accuracy of predicted CFD was assessed using node-wise comparisons. In addition, the ability of Image2Flow to respond to increasing inlet velocities was also evaluated. Image2Flow achieved excellent segmentation accuracy with a median Dice score of 0.91 (IQR: 0.86-0.92). The median node-wise normalized absolute error for pressure and velocity magnitude was 11.75% (IQR: 9.60-15.30%) and 9.90% (IQR: 8.47-11.90), respectively. Image2Flow also showed an expected response to increased inlet velocities with increasing pressure and velocity values. This proof-of-concept study has shown that it is possible to simultaneously perform patient-specific volume-mesh based segmentation and pressure and flow field estimation using Image2Flow. Image2Flow completes segmentation and CFD in ~330ms, which is ~5000 times faster than manual methods, making it more feasible in a clinical environment.

Nationwide synthetic human mobility dataset construction from limited travel surveys and open data

AbstractIn recent years, the explosion of extensive geolocated datasets related to human mobility has presented an opportunity to unravel the mechanism behind daily mobility patterns on an individual and population level; this analysis is essential for solving social matters, such as traffic forecasting, disease spreading, urban planning, and pollution. However, the release of such data is limited owing to the privacy concerns of users from whom data were collected. To overcome this challenge, an innovative approach has been introduced for generating synthetic human mobility, termed as the “Pseudo‐PFLOW” dataset. Our approach leverages open statistical data and a limited travel survey to create a comprehensive synthetic representation of human mobility. The Pseudo‐PFLOW generator comprises three agent models that follow seven fundamental daily activities and captures the spatiotemporal pattern in daily travel behaviors of individuals. The Pseudo‐PFLOW dataset covers the entire population in Japan, approximately 130 million people across 47 prefectures, and has been compared with the existing ground truth dataset. Our generated dataset successfully reconstructs key statistical properties, including hourly population distribution, trip volume, and trip coverage, with coefficient of determination values ranging from 0.5 to 0.98. This innovative approach enables researchers and policymakers to access valuable mobility data while addressing privacy concerns, offering new opportunities for informed decision‐making and analysis.

Do deep learning models accurately measure visual destination image? A comparison of a fine-tuned model to past work

The measurement of destination image from visual media such as online photography is of growing significance to destination managers and marketers who want to make better decisions and attract more visitors to their destination. However, there is no single approach with proven accuracy for doing this. We present a new approach where we fine-tune a deep learning model for a predetermined set of cognitive attributes of destination image. We then train state of the art neural networks using labelled tourist photography and test accuracy by comparing results with a ground truth dataset built for the same set of visual classes. Comparing our fine-tuned model against results which follow past approaches, we demonstrate that the pre-trained models without fine-tuning are not as accurate in capturing all of the destination image’s cognitive attributes. This is, to the best of our knowledge, the first deep learning computer vision model trained specifically to measure the cognitive component of destination image from photography and can act as a benchmark for future systems.

Fake news detection models using the largest social media ground-truth dataset (TruthSeeker)

Fake news detection models using the largest social media ground-truth dataset (TruthSeeker)

The Largest Social Media Ground-Truth Dataset for Real/Fake Content: TruthSeeker

The Largest Social Media Ground-Truth Dataset for Real/Fake Content: TruthSeeker

Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural operators is still data-driven, which needs an expensive ground-truth dataset from various sources (e.g., solving PDEs’ samples with the conventional solvers, real-world experiments) in addition to training stage costs. From a computational perspective, marrying operator learning and specific domain knowledge to solve PDEs is an essential step for data-efficient and low-carbon learning. We propose a novel data-efficient paradigm that provides a unified framework of training neural operators and solving PDEs with the domain knowledge related to the variational form, which we refer to as the variational operator learning (VOL). We develop Ritz and Galerkin approach respectively with finite element discretization for VOL to achieve matrix-free approximation of the energy functional of physical systems and calculation of residual tensors derived from associated linear systems with linear time complexity and O(1) space complexity. We then propose direct minimization and iterative update as two possible optimization strategies. Various types of experiments based on reasonable benchmarks about variable heat source, Darcy flow, and variable stiffness elasticity are conducted to demonstrate the effectiveness of VOL. With a label-free training set, VOL learns solution operators with its test errors decreasing in a power law with respect to the amount of unlabeled data. To the best of the authors’ knowledge, this is the first study that integrates the perspectives of the weak form and efficient iterative methods for solving sparse linear systems into the end-to-end operator learning task. Codes and Datasets are publicly available at https://doi.org/10.5281/zenodo.11097870.