Simulating root length density dynamics of sunflower in saline soils based on machine learning

The growth of rice is a sequence of three different phenological phases. This sequence of change in rice phenology implies that the condition of the plant during the vegetative phase relates directly to the health of leaves functioning during the reproductive and ripening phases. As such, accurate monitoring is important towards understanding rice growth dynamics. Leaf Area Index (LAI) is an important indicator of rice yields and the availability of this information during key phenological phases can support more informed farming decisions. Satellite remote sensing has been adopted as a proxy to field measurements of LAI and with the launch of freely available high resolution Satellite images such as Sentinel-2, it is imperative that accurate retrieval methods are adopted towards monitoring LAI at irrigated rice fields. Here, we evaluate the potential of a hybrid radiative transfer model (i.e., PROSAIL - Gaussian Process Regression (GPR), for estimating the phenological dynamics of irrigated rice LAI using imager derived from the Sentinel-2 multispectral instrument. LAI field measurements were obtained from an experimental rice field in Nasarawa state, Nigeria during the dry season. We used the PROSAIL radiative transfer model to create a look up table (LUT) that was subsequently used to train a GPR model. Afterwards, we evaluated the potential of the hybrid modelling approach by assessing the overall model accuracy and the extent to which LAI was able to accurately predict LAI during key rice phenological phases. We compared the predicted hybrid GPR LAI values with LAI values generated from the SNAP toolbox, based on a hybrid Artificial Neural Network (ANN) modelling approach. Our results show that the overall predictive accuracy of the hybrid GPR model (R2 = 0.82, RMSE = 1.65) was more accurate than that of the hybrid ANN model (R2 = 0.66, RMSE = 3.89) for retrieving LAI values from Sentinel-2 imagery. Both models underestimated LAI values during the reproductive and ripening phases . However, the accuracy during the phenological phases were more significant when using the hybrid GPR model (P < 0.05). During the different phenological phases, the hybrid GPR model predicted LAI more accurately during the reproductive (R2 = 0.7) and ripening (R2 = 0.59) phases compared to the hybrid ANN reproductive and ripening phases. When monitoring LAI phenological profiles of both hybrid models, the hybrid GPR and ANN models underestimated LAI during the reproductive and ripening phases. However, the ANN model underestimations were statistically significantly greater than those for the hybrid GPR model (P < 0.05). Our results highlight the potential of hybrid GPR models for estimating the phenological dynamics of irrigated rice LAI from Sentinel-2 data. They provided more accurate estimation of LAI patterns from varying nitrogen and water applications than hybrid ANN models.

Forecasting short-term solar radiation is crucial for many solar energy applications. Additionally, solar energy has a lower environmental impact than conventional sources like fossil fuels and can be used for investment purposes through the construction of large solar farm facilities. To test, evaluate, and compare various solar radiation models, short-term observations of meteorological, astronomical, computational, and geographical data were collected at two distinct locations from 2012 to 2015. In this study, seven machine learning models were employed: multi-layer perceptron (MLP), feedforward backpropagation algorithm (FFBP), autoregressive integrated moving average (ARIMA), linear regression (LR), radial basis function neural network (RBFNN), random forest (RF), and Gaussian process regression (GPR) models. These models were used to forecast hourly global solar radiation (GSR) using the aforementioned data as model input. The performance of the selected models' forecast accuracy was thoroughly examined by assessing it for a typical day, for four seasons, and under three sky conditions. The RF model can forecast GSR with satisfactory accuracy, and MLP and GPR models provide better accuracy than LR, FFBP, RBF, and ARIMA models. For example, the R2 value range of RF are 0.9621 for Tetuan site and 0.9534 for Tangier site, respectively. Meanwhile, RF, MLP, and GPR models under-forecast few high radiation values on clear days, which may due to the differences in training and testing data ranges and distributions of the sky conditions. Finally, the obtained result of this study indicate that the proposed RF model is a reliable alternative for short-term global solar radiation forecasting due to its high forecast accuracy.

Secondary metabolites have high ecological and economic values. Measuring the amounts of these metabolites in plants through laboratory analysis is time-consuming and expensive. On the other hand, the laboratory results cannot be generalized to a wide area of rangelands with diverse climates, topography, and soil. Therefore, the present study aims to evaluate the potential of PRISMA hyperspectral data to estimate the rangeland phenol concentration at landscape scale in western Isfahan province, Iran. Phenol concentration and spectral signatures were extracted from 42 plant individuals, including Astragalus adscendens, Astragalus verus, Daphne mucronata, Anabasis aphylla, and Phlomis olivieri using laboratory methods and spectroscopy in the range of 350 to 2500 nm. Phenol-sensitive bands were identified by establishing a relationship between phenol concentration and all spectral bands by the Partial Least Square Regression (PLSR) method. The map of phenol spatial changes was then produced with the Bayesian Regularized Artificial Neural Network Model (BRNN), Random Forest (RF), Generalized Linear Model (GAM), Generalized Additive Model (GLM), and Gaussian Process Regression (GPR) in rangelands. The results showed that the phenol concentration in different individuals was between 3.65 and 20.13 (mgGAE/gDW), and species spectral absorptions ranged from 1.650 to 1.660. The very high coefficient of determination of phenol concentration with spectral data (R2 = 0.94) confirmed the use of these data in phenol mapping at the landscape scale. The maximum estimated phenol concentration by GLM, GAM, RF, BRNN, and GPR models was 36.40, 26.76, 18.07, 22.74, and 32.92 GAE/g DW, respectively; which RF model had the highest (R2 = 0.955) and GLM had the lowest accuracy (R2 = 0.816). The findings show that hyperspectral data can estimate secondary metabolites at the landscape scale and can supplement laboratory methods in managing rangeland plants.

In this study, six machine learning (ML) models, namely, random forest (RF), Gaussian process regression (GPR), support vector regression (SVR), decision tree (DT), least squares support vector machine (LSSVM), and multivariate adaptive regression spline (MARS) models, were employed to reconstruct the missing daily‐averaged discharge in a mega‐delta from 1980 to 2015 using upstream‐downstream multi‐station data. The performance and accuracy of each ML model were assessed and compared with the stage‐discharge rating curves (RCs) using four statistical indicators, Taylor diagrams, violin plots, scatter plots, time‐series plots, and heatmaps. Model input selection was performed using mutual information and correlation coefficient methods after three data pre‐processing steps: normalization, Fourier series fitting, and first‐order differencing. The results showed that the ML models are superior to their RC counterparts, and MARS and RF are the most reliable algorithms, although MARS achieves marginally better performance than RF. Compared to RC, MARS and RF reduced the root mean square error (RMSE) by 135% and 141% and the mean absolute error by 194% and 179%, respectively, using year‐round data. However, the performance of MARS and RF developed for the climbing (wet season) and recession (dry season) limbs separately worsened slightly compared to that developed using the year‐round data. Specifically, the RMSE of MARS and RF in the falling limb was 856 and 1,040 m3/s, respectively, while that obtained using the year‐round data was 768 and 789 m3/s, respectively. In this study, the DT model is not recommended, while the GPR and SVR models provide acceptable results.

Gaussian process regression with skewed errors

Su kaynaklarının planlanması ve tarımsal su yönetimi için referans bitki su tüketiminin (ET0) doğru tahmin edilmesi oldukça önemlidir. Bu çalışmada üç farklı makine öğrenimi yönteminin, yapay sinir ağları (YSA), rassal ağaç (RT) ve gauss süreç regresyonu (GPR), yarı nemli iklim koşullarına sahip bir bölgeden alınan iklim verileri kullanılarak günlük ET0’ı tahmin etme performansları araştırılmıştır. Modelleri eğitmek ve test etmek için Bafra’da 2018–2020 döneminde toplanan günlük meteorolojik verilerin beş girdi kombinasyonu [günlük ortalama (Tort), maksimum (Tmax) ve minimum sıcaklık (Tmin), rüzgar hızı (u2), bağıl nem (RHort) ve güneşlenme şiddeti (Rs) hem tam hem de eksik kombinasyonları dahil] kullanılmıştır. Makine öğrenimi modellerinin performansı ise FAO-56 Penman Monteith (FAO-56 PM) standart denklemi ile karşılaştırılmıştır. Modellerin doğruluğunu değerlendirmek için dört farklı istatistiksel performans indeksi kullanılmıştır [belirleme katsayısı (R2), ortalama mutlak hata (MAE), hata kareleri toplamının karekökü (RMSE) ve Nash–Sutcliffe etkinlik katsayısı (NSE)]. Sonuçlar, her beş senaryoda da YSA modellerinin RT ve GPR modellerinden daha iyi performans gösterdiğini ortaya koymuştur. Tüm verilerin girdi olarak kullanıldığı beşinci senaryo için YSA modelleri tarafından tahmin edilen ET0 değerlerinin FAO-56 PM değerleri ile iyi bir uyum içinde olduğu belirlenmiştir (R2=0.988, MAE=0.166, RMSE=0.205, NSE=0.984). Bununla birlikte meteorolojik veriler tam olmadığında bile sadece Tort, RHort ve Rs ile oldukça yüksek günlük ET0 tahminleri elde edilmiştir. Genel olarak, radyasyona dayalı makine öğrenimi modelleri, sıcaklığa dayalı makine öğrenimi modellerinden daha iyi performans göstermiştir. Sonuçlar, yarı nemli iklim özelliklerine sahip bir bölgede YSA modelinin ET0'ı oldukça verimli ve doğru bir şekilde modellemek için etkili bir şekilde kullanılabileceğini göstermektedir.

To predict the potential geographic distribution of Oncomelania hupensis in Yunnan Province using random forest (RF) and maximum entropy (MaxEnt) models, so as to provide insights into O. hupensis surveillance and control in Yunnan Province. The O. hupensis snail survey data in Yunnan Province from 2015 to 2016 were collected and converted into O. hupensis snail distribution site data. Data of 22 environmental variables in Yunnan Province were collected, including twelve climate variables (annual potential evapotranspiration, annual mean ground surface temperature, annual precipitation, annual mean air pressure, annual mean relative humidity, annual sunshine duration, annual mean air temperature, annual mean wind speed, ≥ 0 ℃ annual accumulated temperature, ≥ 10 ℃ annual accumulated temperature, aridity and index of moisture), eight geographical variables (normalized difference vegetation index, landform type, land use type, altitude, soil type, soil textureclay content, soil texture-sand content and soil texture-silt content) and two population and economic variables (gross domestic product and population). Variables were screened with Pearson correlation test and variance inflation factor (VIF) test. The RF and MaxEnt models and the ensemble model were created using the biomod2 package of the software R 4.2.1, and the potential distribution of O. hupensis snails after 2016 was predicted in Yunnan Province. The predictive effects of models were evaluated through cross-validation and independent tests, and the area under the receiver operating characteristic curve (AUC), true skill statistics (TSS) and Kappa statistics were used for model evaluation. In addition, the importance of environmental variables was analyzed, the contribution of environmental variables output by the models with AUC values of > 0.950 and TSS values of > 0.850 were selected for normalization processing, and the importance percentage of environmental variables was obtained to analyze the importance of environmental variables. Data of 148 O. hupensis snail distribution sites and 15 environmental variables were included in training sets of RF and MaxEnt models, and both RF and MaxEnt models had high predictive performance, with both mean AUC values of > 0.900 and all mean TSS values and Kappa values of > 0.800, and significant differences in the AUC (t = 19.862, P < 0.05), TSS (t = 10.140, P < 0.05) and Kappa values (t = 10.237, P < 0.05) between two models. The AUC, TSS and Kappa values of the ensemble model were 0.996, 0.954 and 0.920, respectively. Independent data verification showed that the AUC, TSS and Kappa values of the RF model and the ensemble model were all 1, which still showed high performance in unknown data modeling, and the MaxEnt model showed poor performance, with TSS and Kappa values of 0 for 24%(24/100) of the modeling results. The modeling results of 79 RF models, 38 MaxEnt models and their ensemble models with AUC values of > 0.950 and TSS values of > 0.850 were included in the evaluation of importance of environmental variables. The importance of annual sunshine duration (SSD) was 32.989%, 37.847% and 46.315% in the RF model, the MaxEnt model and their ensemble model, while the importance of annual mean relative humidity (RHU) was 30.947%, 15.921% and 28.121%, respectively. Important environment variables were concentrated in modeling results of the RF model, dispersed in modeling results of the MaxEnt model, and most concentrated in modeling results of the ensemble model. The potential distribution of O. hupensis snails after 2016 was predicted to be relatively concentrated in Yunnan Province by the RF model and relatively large by the MaxEnt model, and the distribution of O. hupensis snails predicted by the ensemble model was mostly the joint distribution of O. hupensis snails predicted by RF and MaxEnt models. Both RF and MaxEnt models are effective to predict the potential distribution of O. hupensis snails in Yunnan Province, which facilitates targeted O. hupensis snail control.

The increasing effects of climate change require the accurate measurement and prediction of carbon emissions from building construction operations. This study aims to assess the performance of Gaussian Process Regression (GPR) and Support Vector Machine (SVM) in predicting emissions and determine which model is best suited for improving sustainable construction practices. The GPR and SVM models were trained and tested using empirical datasets with varying parameter values. Model performance is evaluated using correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE). The analysis reveals that GPR consistently performs better than SVM across diverse datasets, especially in intricate and varied data situations. The superior performance of GPR highlights its robustness and versatility in handling the complexities of construction-related emissions data. The results indicate that GPR has the potential to assist significantly many stakeholders in the construction sector, including planners and environmental managers, in making better-informed decisions that are in line with carbon reduction objectives. Further studies could examine the incorporation of further predictive variables into the GPR model, such as economic indicators and the effects of material innovation.

The Gaussian process regression (GPR) model, which is a powerful machine learning tool for probabilistic prediction, is introduced into slope displacement prediction. Using this model, the displacements of the slope of the permanent ship lock of the Three Gorges Project, the Wolongsi slope, and the high slope of Longtan hydropower station were predicted. In addition, the predictive uncertainty index (PUI) for describing the uncertainty of the predicted results was proposed, and the corresponding classification of the PUI was established. The study results demonstrate that the GPR model can self-adaptively acquire model parameter values and has satisfactory adaptability for predicting nonlinear time series of slope displacement. The proposed PUI and its classification based on the GPR model enable quantitative uncertainty analysis and, in turn, reliability evaluation of the predicted results. The GPR model provides a new approach to displacement prediction and safety management in slope engineering.

Gaussian process regression to determine water content of methane: Application to methane transport modeling

Due to the recent advances in digitisation of the manufacturing industry and the generation of manufacturing data, there is increasing interest to integrate machine learning on the shop floor to improve efficiency and quality control. Ultrasonic welding is an emerging joining process used in various manufacturing industries, and is an energy efficient, cost-effective method of joining similar or dissimilar materials. However, the quality of the joint achievable is heavily dependent on process input parameters. In this study, a Gaussian Process Regression (GPR) model is developed to map the relationship between process parameters and joint performance for ultrasonically welded aluminium joints, with a view to improving quality control in a manufacturing setting. Initially, a 33 full factorial design of experiments is conducted to investigate the influential parameters, then a GPR model is trained on the experimental data. In-process sensor data is also used to infer process performance. To assess the prediction performance of the model, ten unseen parameter combinations are predicted and compared to their respective experimental result. The model demonstrates a high level of accuracy producing a Pearson’s correlation coefficient of 0.982 between the predicted and actual results for all data. The mean relative predictive error for unseen data is 7.35%.KeywordsUltrasonic weldingMachine learningGaussian process regressionQuality control

Precise and timely leaf area index (LAI) estimation for winter wheat is crucial for precision agriculture. The emergence of high-resolution unmanned aerial vehicle (UAV) data and machine learning techniques offers a revolutionary approach for fine-scale estimation of wheat LAI at the low cost. While machine learning has proven valuable for LAI estimation, there are still model limitations and variations that impede accurate and efficient LAI inversion. This study explores the potential of classical machine learning models and deep learning model for estimating winter wheat LAI using multispectral images acquired by drones. Initially, the texture features and vegetation indices served as inputs for the partial least squares regression (PLSR) model and random forest (RF) model. Then, the ground-measured LAI data were combined to invert winter wheat LAI. In contrast, this study also employed a convolutional neural network (CNN) model that solely utilizes the cropped original image for LAI estimation. The results show that vegetation indices outperform the texture features in terms of correlation analysis with LAI and estimation accuracy. However, the highest accuracy is achieved by combining both vegetation indices and texture features to invert LAI in both conventional machine learning methods. Among the three models, the CNN approach yielded the highest LAI estimation accuracy (R 2 = 0.83), followed by the RF model (R 2 = 0.82), with the PLSR model exhibited the lowest accuracy (R 2 = 0.78). The spatial distribution and values of the estimated results for the RF and CNN models are similar, whereas the PLSR model differs significantly from the first two models. This study achieves rapid and accurate winter wheat LAI estimation using classical machine learning and deep learning methods. The findings can serve as a reference for real-time wheat growth monitoring and field management practices.

Machine learning (ML) force fields are revolutionizing molecular dynamics (MD) simulations as they bypass the computational cost associated with ab initio methods but do not sacrifice accuracy in the process. In this work, the GPyTorch library is used to create Gaussian process regression (GPR) models that are interfaced with the next-generation ML force field FFLUX. These models predict atomic properties of different molecular configurations that appear in a progressing MD simulation. An improved kernel function is utilized to correctly capture the periodicity of the input descriptors. The first FFLUX molecular simulations of ammonia, methanol, and malondialdehyde with the updated kernel are performed. Geometry optimizations with the GPR models result in highly accurate final structures with a maximum root-mean-squared deviation of 0.064 Å and sub-kJ mol-1 total energy predictions. Additionally, the models are tested in 298 K MD simulations with FFLUX to benchmark for robustness. The resulting energy and force predictions throughout the simulation are in excellent agreement with ab initio data for ammonia and methanol but decrease in quality for malondialdehyde due to the increased system complexity. GPR model improvements are discussed, which will ensure the future scalability to larger systems.

Over the last decade, innovations in satellite remote sensing (RS) and data science have widened the scope and relevance of agricultural monitoring and management applications at farm and territorial scales. Recently launched and upcoming hyperspectral satellite missions (e.g., ASI-PRISMA, DLR-ENMAP, Planet-Tanager, ESA-CHIME, Kuva-Hyperfield) provide high spectral resolution (&lt; 10 nm) across the 400-2500 nm range, opening new frontiers for assessing biophysical and biochemical functional traits of agroecosystems, while advancements in machine learning (ML) and artificial intelligence (AI) allow the efficient exploitation of the information content of high-dimensionality spectral datasets. Here we summarize the results and lessons learned from three experiments in different European agricultural systems (croplands and grasslands), analysing how the synergy between hyperspectral imaging spectroscopy (field and satellite), ML, and foundation models could support adaptive agroecosystem management through the retrieval of vegetation and soil properties related to the nutrient cycle. The three case studies are:(1) Assessment of biomass and nutritional quality of Alpine pastures: Gaussian Process Regression (GPR) models were calibrated on 250 vegetation samples and field spectra collected in 2024 and 2025 from semi-natural pastures in Valtournanche (Aosta, Italy) and Val Camonica (Brescia, Italy). PRISMA-derived maps for biomass and leaf-level protein, and fiber content showed good accuracy against in-situ data (LAI [-] R2 = 0.71, RMSE = 0.89; Biomass [g · m-2] R2 = 0.67, RMSE = 178.71; DM [%] R2 = 0.65, RMSE = 2.70; CP [%] R2 = 0.58, RMSE = 0.52; ADF [%] R2 = 0.45, RMSE = 2.42; NDF [%] R2 = 0.50, RMSE = 0.61), allowing mapping of pasture metabolizable energy in support of grazing management.(2) Monitoring of nutritional status of paddy fields: GPR models were developed on 200 vegetation samples and field spectra collected in 2024 and 2025 in several fields located in the Ferrara region (Italy). These models, demonstrated on PRISMA and EnMAP time-series, effectively monitored crop development across a temporally and spatially independent test set (LAI [-] R2 = 0.83, RMSE = 0.30; Fresh Biomass [g · m-2] R2 = 0.72, RMSE = 627.67; LCC [μg · cm-2] R2 = 0.58, RMSE = 3.40; LNC [μg · cm-2] R2 = 0.34, RMSE = 22.51; CNC [g · m-2] R2 = 0.56, RMSE = 0.77).(3) Retrieval of Soil Organic Carbon (SOC) and soil Nitrogen (N) on arable lands: A transformer-based, sensor-agnostic deep learning architecture was fine-tuned on open global spectral libraries. When applied to EMIT and Tanager-1 imagery over the Po Plain (Italy) and Northern Netherlands regions, the model yielded high accuracy (SOC [%] R2 = 0.61, MAE = 0.37; N [%] R2 = 0.68, MAE = 0.12) against 289 independent field observations.Our findings demonstrate that satellite hyperspectral spectroscopy can complement operational multi-spectral missions, adding key information about agroecosystems nutritional status. Furthermore, we show that the use of pre-trained ML and AI models on global spectral libraries and field reflectance data allows accurate retrieval even in the absence of ground truth acquisition synchronous to the satellite overpass, offering a potential scalable solution for agroecosystems management and monitoring at landscape scale.

Active learning sensitivity analysis of γ'(L12) precipitate morphology of ternary co-based superalloys