Gaussian Process Research Articles

Optimizing papermaking wastewater treatment by predicting effluent quality with node-level capsule graph neural networks.

Papermaking wastewater consists of a sizable amount of industrial wastewater; hence, real-time access to precise and trustworthy effluent indices is crucial. Because wastewater treatment processes are complicated, nonlinear, and time-varying, it is essential to adequately monitor critical quality indices, especially chemical oxygen demand (COD). Traditional models for predicting COD often struggle with sensitivity to parameter tuning and lack interpretability, underscoring the need for improvement in industrial wastewater treatment. In this manuscript, an optimized papermaking wastewater treatment method is proposed that predicts effluent quality using node-level capsule graph neural networks (PWWT-PEQ-NLCGNN). To improve the accuracy of predicting important effluent COD quality indices, the NLCGNN weight parameters are optimized using the hermit crab optimization (HCO) algorithm. The performance of the proposed PWWT-PEQ-NLCGNN technique demonstrated improvements over existing techniques. Specifically, the proposed strategy achieved 30.53%, 23.34%, and 32.64% higher accuracy; 20.53%, 25.34%, and 29.64% higher precision; and 20.53%, 25.34%, and 29.64% higher sensitivity compared to the water quality prediction model using Gaussian process regression based on deep learning for carbon neutrality in papermaking wastewater treatment system (WQP-GPR-DL-CLPWWTS), the prediction of effluent quality in papermaking wastewater treatment processes using dynamic kernel-based extreme learning machine (POEQ-PWWTP-DKBELM), and the quality-related monitoring of papermaking wastewater treatment processes using dynamic multi-block partial least squares (QRM-PWWTP-DMPLS). These results highlight the potential of the PWWT-PEQ-NLCGNN method for enabling timely and accurate monitoring of wastewater treatment processes.

Efficient modeling of quasi-periodic data with seasonal Gaussian process

Efficient modeling of quasi-periodic data with seasonal Gaussian process

Uncertainty-Based Industrial Water Supply and Demand Balance Pattern Recognition: A Case Study in the Yellow River Basin of Gansu Province, China

The balance between water supply and demand is essential for industrial growth, affecting economic, social, and environmental sustainability. Our research employs a Gaussian process regression for demand prediction. Additionally, it takes into account water limits and policy thresholds when determining the supply, thereby defining a range of uncertainty for both the industrial demand and the supply. A pattern recognition method matches this trade-off range, identifying three patterns to support water management. The study focuses on the analysis of industrial water supply and demand dynamics under uncertain conditions in nine cities (Baiyin, Dingxi, Gannan, Lanzhou, Linxia, Pingliang, Qingyang, Tianshui, and Wuwei) in Gansu Province of China’s Yellow River Basin in 2030. The results of the study show that industrial water use in Baiyin, Linxia, Dingxi, and Tianshui cities falls into Pattern I, providing water resources to support industrial development. Industrial water use in Wuwei, Pingliang, Qingyang, and Gannan cities represents Pattern II, which maintains a balance between supply and demand while allowing flexibility in water demand. Finally, the industrial water use in Lanzhou city is characterized by Pattern III, which requires optimization through structural, technological, and management improvements to mitigate the negative impacts of water scarcity on the sustainable development of the economy and society. The results of the research can be used as a reference for policy making in water resources planning and management in the basin.

Gaussian Process Regression with a Hybrid Risk Measure for Dynamic Risk Management in the Electricity Market

In this work, we introduce an innovative approach to managing electricity costs within Germany’s evolving energy market, where dynamic tariffs are becoming increasingly normal. In line with recent German governmental policies, particularly the Energiewende (Energy Transition) and European Union directives on clean energy, this work introduces a risk management strategy based on a combination of the well-known risk measures of the Value at Risk (VaR) and Conditional Value at Risk (CVaR). The goal is to optimize electricity procurement by forecasting hourly prices over a certain horizon and allocating a fixed budget using the aforementioned measures to minimize the financial risk. To generate price predictions, a Gaussian process regression model is used. The aim of this hybrid approach is to design a model that is easily understandable but allows for a comprehensive evaluation of potential financial exposure. It enables consumers to adjust their consumption patterns or market traders to invest and allows more cost-effective and risk-aware decision-making. The potential of our approach is shown in a case study based on the German market. Moreover, by discussing the political and economical implications, we show how the implementation of our method can contribute to the realization of a sustainable, flexible, and efficient energy market, as outlined in Germany’s Renewable Energy Act.

Experimental and analytical study on axial behaviour of square corrugated concrete filled single and double skin tube stub columns

Concrete-filled double-skin steel tubular (CFDST) columns have become widely utilized in building construction and bridges, thanks to their exceptional structural capabilities. Therefore, this study investigates the axial compressive behavior of square CFDST columns. The study aims to explore the influence of external and internal plate shapes (flat or corrugated plates) and different widths of internal steel tubes on the axial compressive behavior. The effects of varying internal widths of the internal steel tube (60 mm, 116 mm, and 160 mm) on the performance of CFDST columns were examined. Additionally, the study compared the performance of concrete-filled steel tubular (CFST) and CFDST columns with external flat or corrugated plates. The findings indicated that incorporating internal corrugated plates notably improved both the load-carrying capacity and ductility of the specimens. Notably, CFDST columns featuring corrugated internal plates (116 mm width) exhibited strength enhancements of 25.3% and 7.4% compared to internal widths of 160 mm and 60 mm, respectively. Furthermore, the study proposed two machine-learning models, namely Artificial Neural Network (ANN) and Gaussian Process Regression (GPR), to estimate the ultimate compressive strength of square CFDST columns. The findings indicated that the GPR model outperformed the ANN model in predicting the bearing capacity of square CFDST columns. Additionally, the Shapley Additive Explanation technique was employed for feature analysis. The outcomes of this analysis revealed that parameters such as section width and concrete strength positively influence the compressive strength index.

Rapid Identification of Saline–Alkali Stress-Tolerant Peanut Varieties Based on Multimodal Data

The cultivation of saline–alkali-tolerant peanut (Arachis hypogaea L.) varieties can effectively increase grain yield in saline–alkali land. However, traditional assessment methods are often cumbersome and time consuming. To rapidly identify saline–alkali stress-tolerant peanut varieties, this research proposed a saline–alkali stress tolerance evaluation method based on deep learning and multimodal data. Specifically, the research first established multimodal datasets for peanuts at different growth stages and constructed a saline–alkali stress score standard based on unsupervised learning. Subsequently, a deep learning network called BO-MFFNet was built and its structure and hyperparameters were optimized by the Bayes optimization (BO) algorithm. Finally, the point prediction of the saline–alkali stress score were carried out by using the Gaussian process regression model. The experimental results show that the multimodal method is superior to the single-modal data and the BO algorithm significantly improves the performance of the model. The root mean squared error and relative percentage deviation of the BO-MFFNet model are 0.089 and 3.669, respectively. The model effectively predicted the salt–alkali stress tolerance of five varieties, and the predicted results were Huayu25, Yuhua31, Yuhua33, Yuhua32, and Yuhua164 from high to low. This research provides a new method for assessing crop tolerance under extreme environmental stress.

An ML-Enhanced Laser-Based Methane Slip Sensor Using Wavelength Modulation Spectroscopy.

Natural gas (NG) is a promising alternative to diesel for sustainable transport, potentially reducing GHG and air quality emissions significantly. However, the GHG benefits hinge on managing methane slip, the unburned methane in the exhaust of NG engines, which carries a significant global warming potential. The CH4 slip from NG engines is highly dependent on engine type and operation, and effective greenhouse gas emission mitigation requires that the actual operation of real-world engines is monitored. This requires suitable instrumentation for online robust CH4 measurement in engine exhaust. Traditional methane slip measurement methods need frequent calibration, may not be suited to dynamic operational conditions, carry significant costs, or require expert users. Furthermore, the significant computational demands associated with calibration-free spectroscopic methods and the prevalent noise uncertainty underscore the urgent requirement for innovative sensors. These sensors must not only respond rapidly but also have low uncertainty in their readings. This paper presents a machine learning (ML)-enhanced, laser-based methane slip sensor using wavelength modulation spectroscopy (WMS) for rapid, accurate, and calibration-free CH4 measurements for application in the exhaust of NG engines. The sensor utilizes a distributed feedback (DFB) laser diode emitting around 1.65 μm propagated through a multipass optical cell. An ML-based approach is used to invert the recorded WMS signal, which reduces computational cost and uncertainty due to noise vulnerabilities inherent in traditional measurement inversion approaches. A Gaussian process regression (GPR) model, trained on measured and simulated WMS signals, was selected for its high predictive accuracy, where it achieved a mean absolute percent error (MAPE) of 0.24%. For exhaust measurement on an in-use natural gas marine vessel, a mean absolute difference of 3.95% was observed, relative to simultaneous reference Fourier transform infrared spectroscopy measurements. The ML-based WMS inversion system marks a significant advancement in methane slip measurement, offering real-time monitoring capabilities with reduced computational demands. Its development supports the realization of NG environmental benefits for transport by providing accurate CH4 slip data, which are essential for engine performance optimization, regulatory adherence, and sustainable policy decisions.

A Joint Prediction of the State of Health and Remaining Useful Life of Lithium-Ion Batteries Based on Gaussian Process Regression and Long Short-Term Memory

To comprehensively evaluate the current and future aging states of lithium-ion batteries, namely their State of Health (SOH) and Remaining Useful Life (RUL), this paper proposes a joint prediction method based on Gaussian Process Regression (GPR) and Long Short-Term Memory (LSTM) networks. First, health features (HFs) are extracted from partial charging data. Subsequently, these features are fed into the GPR model for SOH estimation, generating SOH predictions. Finally, the estimated SOH values from the initial cycle to the prediction start point (SP) are input into the LSTM network in order to predict the future SOH trajectory, identify the End of Life (EOL), and infer the RUL. Validation on the Oxford Battery Degradation Dataset demonstrates that this method achieves high accuracy in both SOH estimation and RUL prediction. Furthermore, the proposed approach can directly utilize one or more health features without requiring dimensionality reduction or feature fusion. It also enables RUL prediction at the early stages of a battery’s lifecycle, providing an efficient and reliable solution for battery health management. However, this study is based on data from small-capacity batteries and does not yet encompass applications in large-capacity or high-temperature scenarios. Future work will focus on expanding the data scope and validating the model’s performance in real-world systems, driving its application in practical engineering scenarios.

Modeling Path Effects Due to 3D Velocity Structure for Nonergodic Ground-Motion Models: A Case Study Using Turkish Ground-Motion Data

ABSTRACT The objective of this study is to assess the performance of different path-effect models for developing nonergodic ground motion models (GMMs) using a Turkish ground-motion database. The cell-specific attenuation approach is widely used to capture path effects in the formulation of nonergodic GMMs. However, this approach can mainly capture anelastic attenuation effects associated with the spatial variation of the quality factor, and it is limited in capturing 3D velocity structure effects, which may be, in particular, relevant for long-period ground motions or short-distance and short-period ground motions. Recent efforts have introduced new models to incorporate 3D velocity structure effects; however, the assessment of these models in the context of instrumentally recorded ground motions is limited. This study assesses the performance of three path-effects models for Türkiye. Specifically, we consider the cell-specific attenuation approach and two additional models based on Gaussian processes but with a different parametrization on how they represent the spatial correlation of path effects. The results indicate that the models based on Gaussian processes outperform the cell-specific approach for long-period spectral accelerations and short-period ground motions at short distances, offering significant aleatory standard deviation reductions. The differences between the Gaussian process-based models are also discussed, highlighting how their parameterization is reflected in prediction patterns. This study contributes to the transition from ergodic to nonergodic approaches in performance-based earthquake engineering.

Accurate machine learning of rate coefficients for state-to-state transitions in molecular collisions.

We present an algorithm that combines quantum scattering calculations with probabilistic machine-learning models to predict quantum dynamics rate coefficients for a large number of state-to-state transitions in molecule-molecule collisions much faster than with direct solutions of the Schrödinger equation. By utilizing the predictive power of Gaussian process regression with kernels, optimized to make accurate predictions outside of the input parameter space, the present strategy reduces the computational cost by about 75%, with an accuracy within 5%. Our method uses temperature dependences of rate coefficients for transitions from the isolated states of initial rotational angular momentum j, determined via explicit calculations, to predict the temperature dependences of rate coefficients for other values of j. The approach, demonstrated here for rovibrational transitions of SiO due to thermal collisions with H2, uses different prediction models and is thus adaptive to various time and accuracy requirements. The procedure outlined in this work can be used to extend multiple inelastic molecular collision databases without exponentially large computational resources required for conventional rigorous quantum dynamics calculations.

Hyperspectral estimation of chlorophyll density in winter wheat using fractional-order derivative combined with machine learning

Chlorophyll density (ChD) can reflect the photosynthetic capacity of the winter wheat population, therefore achieving real-time non-destructive monitoring of ChD in winter wheat is of great significance for evaluating the growth status of winter wheat. Derivative preprocessing has a wide range of applications in the hyperspectral monitoring of winter wheat chlorophyll. In order to research the role of fractional-order derivative (FOD) in the hyperspectral monitoring model of ChD, this study based on an irrigation experiment of winter wheat to obtain ChD and canopy hyperspectral reflectance. The original spectral reflectance curves were preprocessed using 3 FOD methods: Grünwald-Letnikov (GL), Riemann-Liouville (RL), and Caputo. Hyperspectral monitoring models for winter wheat ChD were constructed using 8 machine learning algorithms, including partial least squares regression, support vector regression, multi-layer perceptron regression, random forest regression, extra-trees regression (ETsR), decision tree regression, K-nearest neighbors regression, and gaussian process regression, based on the full spectrum band and the band selected by competitive adaptive reweighted sampling (CARS). The main results were as follows: For the 3 types of FOD, GL-FOD was suitable for analyzing the change process of the original spectral curve towards the integer-order derivative spectral curve. RL-FOD was suitable for constructing the hyperspectral monitoring model of winter wheat ChD. Caputo-FOD was not suitable for hyperspectral research due to its insensitivity to changes in order. The 3 FOD calculation methods could all improve the correlation between the original spectral curve and Log(ChD) to varying degrees, but only the GL method and RL method could observe the change process of correlation with order changes, and the shorter the wavelength, the smaller the order, and the higher the correlation. The bands screened by CARS were distributed throughout the entire spectral range, but there was a relatively concentrated distribution in the visible light region. Among all models, CARS was used to screen bands based on the 0.3-order RL-FOD spectrum, and the model constructed using ETsR reached the best accuracy and stability. Its R2c, RMSEc, R2v, RMSEv, and RPD were 1.0000, 0.0000, 0.8667, 0.1732, and 2.6660, respectively. In conclusion, based on the winter wheat ChD data set and the corresponding canopy hyperspectral data set, combined with 3 FOD calculation methods, 1 band screening method, and 8 modeling algorithms, this study constructed hyperspectral monitoring models for winter wheat ChD. The results showed that based on the 0.3-order RL-FOD, combined with the CARS screening band, ETsR modeling has the highest accuracy, and hyperspectral estimation of winter wheat ChD can be realized. The results of this study can provide some reference for the rapid and nondestructive estimation of ChD in winter wheat.

Towards a shape-performance integrated digital twin for lumbar spine analysis

Background With significant advancement and demand for digital transformation, the digital twin has been gaining increasing attention as it is capable of establishing real-time mapping between physical space and virtual space. In this work, a digital twin solution is presented to predict the real-time biomechanics of the lumbar spine during human movement. Methods A finite element model (FEM) of the lumbar spine was firstly developed using computed tomography (CT) and constrained by the body movement which calculated by the inverse kinematics algorithm. The Gaussian process regression was utilized to train the predicted results and create the digital twin of the lumbar spine in real-time. Finally, a three-dimensional virtual reality system was developed using Unity3D to display and record the real-time biomechanics performance of the lumbar spine during body movement. Results The evaluation results presented an agreement (R 2 >0.8) between the real-time prediction from digital twin and offline FEM prediction. Conclusions This approach provides an effective method of real-time planning and warning in spine rehabilitation.

Updating pile bearing capacity estimation using multiple piling data and spatial correlation

ABSTRACT This paper proposes a method to comprehensively capture the variability of pile bearing capacity from the piling data within a site by Bayesian Gaussian process regression. The approach, based on the assumption that multiple piles are installed under controlled piling conditions, involves steps from obtaining piling data to calculating a credible interval on pile bearing capacity, considering spatial variability, piling variation and estimation error. To validate the proposed method, a field test was conducted with rotary cutting press-in piles. Three different input data and estimation methods were used, and their estimates were compared with rapid load test measurements. The proposed method successfully provided credible intervals that appropriately contained the measured values, and the estimated variances were generally in good agreement. The residuals of the estimation error fit the log-normal distribution well. The validity of the proposed method was confirmed for all three piling data inputs, demonstrating its versatility. Furthermore, the proposed method reduces the statistical error when identifying bias from comparisons with load tests. It would also increase the value of piling data, which has traditionally been difficult to use for small projects due to the requirement of additional load tests to identify inter-site errors in the piling data.

Gaussian Process-Based Robust Optimization with Symmetry Modeling and Variable Selection

Gaussian process (GP)-based robust optimization is an effective tool in product quality improvement. However, most existing variable selection methods are designed for parametric models and are unsuitable for nonparametric GP models. Additionally, improving the prediction accuracy of GP models with limited design points remains a significant challenge in robust optimization. To address these issues, this article proposes a GP-based multi-stage robust parameter optimization method that integrates symmetry modeling, sensitivity analysis (SA), and Markov Chain Monte Carlo (MCMC) techniques. First, a modified expected improvement (EI) criterion is introduced to enhance the utilization efficiency of design points. Second, a nonparametric variable selection technique based on SA is developed for GP models to identify significant variables. This method considers both independent variables and their interactions, improving the interpretability of GP models. Finally, the selected variables are used to construct the robust optimization model, and the genetic algorithm (GA) is employed to search for the optimal solution within the feasible domain. Numerical simulations and real-world experiments demonstrate the effectiveness of the proposed method. Comparative results indicate that the proposed method obtains more robust optimal input parameter settings compared to existing approaches.

Density prediction for selective laser melting fabricated of CuCrZr alloy using hybrid Gaussian boosted regression

Selective laser melting (SLM), an emerging technology, constructs components through layer-by-layer material deposition and has gained popularity in the industry due to its advantages such as shorter lead time, higher flexibility, lower material wastage, and the capability to fabricate complex geometries. However, the development of process databases for new materials is often time-consuming and laborious because SLM involves multiple physical fields and multiple process steps with numerous process parameters. Recently, machine learning is renowned for its excellent capabilities in tasks such as classification, regression, and clustering. In this study, hybrid Gaussian boosted regression that combines Gaussian process regression with gradient boosting machine was used to obtain a process database for CuCrZr alloy, optimizing for density with laser power and scanning speed as characteristic parameters, under limited samples. A machine learning model was developed using fivefold cross-training on 36 datasets. With a determination coefficient (R2) of 0.96587, the model demonstrated a high level of fit. Next, by extending the prediction range, we achieved process parameters for the highest five densities of samples. Finally, the model’s precision was confirmed with experiments on the five predicted maximum densities, with all predictions falling within a ±0.09% error margin from the experimental values. This research precisely predicted the densities of SLM-formed CuCrZr parts, created a comprehensive process parameter database, and substantiated both theoretical and practical backing for the 3D printing of CuCrZr parts.

A Weighted Bayesian Kernel Machine Regression Approach for Predicting the Growth of Indoor-Cultured Abalone

The cultivation of abalone, a species with high economic value, faces significant challenges due to its slow growth rate and sensitivity to environmental conditions, resulting in prolonged cultivation periods and increased mortality risks. To address these challenges, we propose a novel probabilistic machine learning approach based on a Bayesian framework to predict abalone growth by modeling key environmental factors, including water temperature, pH, salinity, nutrient supply, and dissolved oxygen levels. The proposed method employs a weighted Bayesian kernel machine regression model, integrating Gaussian processes with a spike-and-slab prior to identify influential variables. This approach accommodates heteroscedasticity, capturing varying levels of variance across observations, and models complex, non-linear relationships between environmental factors and abalone growth. Our analysis reveals that time, dissolved oxygen, salinity, and nutrient supply are the most critical factors influencing growth, while water temperature and pH play relatively minor roles under controlled indoor farming conditions. Interaction analysis highlights the non-linear dependencies among factors, such as the combined effects of salinity and nutrient supply. The proposed model not only improves prediction accuracy compared to baseline methods, but also provides actionable insights into the environmental dynamics that optimize abalone growth. These findings underscore the potential of advanced machine learning techniques in enhancing aquaculture practices and offer a robust framework for managing complex, multi-variable systems in sustainable farming.

Forecasting geothermal temperature in western Yemen with Bayesian-optimized machine learning regression models

Geothermal energy is a sustainable resource for power generation, particularly in Yemen. Efficient utilization necessitates accurate forecasting of subsurface temperatures, which is challenging with conventional methods. This research leverages machine learning (ML) to optimize geothermal temperature forecasting in Yemen’s western region. The data set, collected from 108 geothermal wells, was divided into two sets: set 1 with 1402 data points and set 2 with 995 data points. Feature engineering prepared the data for model training. We evaluated a suite of machine learning regression models, from simple linear regression (SLR) to multi-layer perceptron (MLP). Hyperparameter tuning using Bayesian optimization (BO) was selected as the optimization process to boost model accuracy and performance. The MLP model outperformed others, achieving high R2 values and low error values across all metrics after BO. Specifically, MLP achieved R2 of 0.999, with MAE of 0.218, RMSE of 0.285, RAE of 4.071%, and RRSE of 4.011%. BO significantly upgraded the Gaussian process model, achieving an R2 of 0.996, a minimum MAE of 0.283, RMSE of 0.575, RAE of 5.453%, and RRSE of 8.717%. The models demonstrated robust generalization capabilities with high R2 values and low error metrics (MAE and RMSE) across all sets. This study highlights the potential of enhanced ML techniques and the novel BO in optimizing geothermal energy resource exploitation, contributing significantly to renewable energy research and development.

Improvement of Citrus Yield Prediction Using UAV Multispectral Images and the CPSO Algorithm

Achieving timely and non-destructive assessments of crop yields is a key challenge in the agricultural field, as it is important for optimizing field management measures and improving crop productivity. To accurately and quickly predict citrus yield, this study obtained multispectral images of citrus fruit maturity through an unmanned aerial vehicle (UAV) and extracted multispectral vegetation indices (VIs) and texture features (T) from the images as feature variables. Extreme gradient boosting (XGB), random forest (RF), support vector machine (SVM), gaussian process regression (GPR), and multiple stepwise regression (MSR) models were used to construct citrus fruit number and quality prediction models. The results show that, for fruit number prediction, the XGB model performed best under the combined input of VIs and T, with an R2 = 0.792 and an RMSE = 462 fruits. However, for fruit quality prediction, the RF model performed best when only the VIs were used, with an R2 = 0.787 and an RMSE = 20.0 kg. Although the model accuracy was acceptable, the number of input feature variables used was large. To further improve the model prediction performance, we explored a method that utilizes a hybrid coding particle swarm optimization algorithm (CPSO) coupled with XGB and SVM models. The coupled models had a significant improvement in predicting the number and quality of citrus fruits, especially the model of CPSO coupled with XGB (CPSO-XGB). The CPSO-XGB model had fewer input features and higher accuracy, with an R2 > 0.85. Finally, the Shapley additive explanations (SHAP) method was used to reveal the importance of the normalized difference chlorophyll index (NDCI) and the red band mean feature (MEA_R) when constructing the prediction model. The results of this study provide an application reference and a theoretical basis for the research on UAV remote sensing in relation to citrus yield.

A Gaussian process model for capturing digital divide in mobile app usage: the role of habit formation

ABSTRACT Natural disasters, such as COVID-19, may have reinforced the digital divide among various population groups. Drawing on the regulatory focus theory, this study proposes a Gaussian process model to capture the dynamics of the ‘second-level digital divide’ over 14 months during a natural crisis, namely the COVID-19 pandemic. The findings indicate that the pandemic reduced the digital divide among mobile users across different age groups. Additionally, the analysis identifies habit formation as a factor that could mitigate the digital divide. This study offers recommendations to reduce the digital divide and promote digital inclusion for older people in the post-pandemic world, should society face a recurrence of COVID-19 or another pandemic outbreak in the future.

Application of Developing Artificial Intelligence (AI) Techniques to Model Pan Evaporation Trends in Slovak River Sub-Basins

The modeling of pan evaporation (Ep) trends in Slovak river sub-basins was conducted using advanced artificial intelligence (AI) techniques algorithms to accurately calculate evaporation rates based on daily climate data from 2010 to 2023 across eight sub-basins in the Slovak Republic. The AI modeling results reveal that the Bodrog, Hornád, Ipeľ, Morava, Slaná, and Váh river basins are experiencing increases in evaporation, while the Dunaj and Hron rivers show declining trends. This divergence may indicate varying ecological factors influencing the evaporation dynamics of each river. A comprehensive set of 28 machine learning (ML) and deep learning (DL) models was employed, including ML techniques such as linear regression, tree-based, support vector machines (both with and without kernels), ensemble, and Gaussian process methods; as well as DL approaches like neural networks (narrow, medium, wide, bilayered, and trilayered). Among these, stepwise linear regression provided the most optimal fit. The minimum redundancy maximum relevance (mRMR) method was utilized for feature selection to balance relevance and redundancy effectively. The results suggest that emphasizing relative humidity (RH) and minimum temperature (tmin) significantly enhances accuracy, highlighting the critical roles of these factors in modeling pan evaporation trends. The results offer precise evaporation analyses to improve water management and lessen scarcity.