Gaussian Process Regression Approach Research Articles

Reliable smart models for estimating frictional pressure drop in two-phase condensation through smooth channels of varying sizes

Reliable and comprehensive predictive tools for the frictional pressure drop (FPD) are of particular importance for systems involving two-phase flow condensation. However, the available models are only applicable to specific operating conditions and channel sizes. Thus, this study aims at developing universal models to estimate the FPD during condensation inside smooth mini/micro and conventional (macro) channels. An extensive databank, comprising 8037 experimental samples and 23 working fluids from 50 reliable sources, was prepared to achieve this target. A comprehensive investigation on the literature models reflected the fact that all of them are associated with high deviations, and their average absolute relative errors (AAREs) exceed 26%. Hence, after identifying the most effective input variables through the Spearman's correlation analysis, three soft-computing paradigms, i.e., multilayer perceptron (MLP), gaussian process regression (GPR) and radial basis function (RBF) were employed to establish intelligent and dimensionless predictive tools for the FPD based on the separated model suggested by Lockhart and Martinelli. Among them, the most accurate results were presented by the GPR approach with AARE and R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{2}$$\\end{document} values of 4.10%, 99.23% respectively, in the testing step. The truthfulness and applicability of the models were explored through an array of statistical and visual analyses, and the results affirmed the obvious superiority of the newly proposed approaches over the literature correlations. Furthermore, the novel predictive tools excellently described the physical variations of the condensation FPD versus the operating parameters. Ultimately, the order of importance of factors in controlling the condensation FPD was clarified by a sensitivity analysis.

The Enhanced Adsorption Capacity of Ziziphus jujuba Stones Modified with Ortho-Phosphoric Acid for Organic Dye Removal: A Gaussian Process Regression Approach

Here, the chemical modification of Ziziphus jujuba stones (ZJS) treated with ortho-phosphoric acid (ZJS-H3PO4) is investigated to enhance its adsorption properties for organic dyes. The physicochemical properties of ZJS-H3PO4 reveal increased porosity (87.29%), slightly higher bulk density (0.034 g mL−1), and enhanced acidity (31.42 m eq g g−1) compared to untreated ZJS. XRF analysis confirms the successful incorporation of orthophosphoric acid during treatment due to a significant increase in phosphorus content. The maximum adsorption capacity of methylene blue on ZJS-H3PO4 is found to be 179.83 mg g−1, demonstrating its efficacy as a potential adsorbent for organic dyes. These findings suggest that modifying ZJS with orthophosphoric acid could be a promising strategy to enhance its adsorption performance in various environmental applications. Furthermore, Gaussian process regression (GPR) is employed to model MB adsorption by ZJS-H3PO4. Optimization of the GPR model involves evaluating different kernel functions and meticulously adjusting parameters to maximize its ability to capture complex relationships in the data. The obtained GPR model demonstrates remarkable performance with high correlation coefficients (R) and low root mean square errors (RMSEs) across all study phases. Model validation is performed through residual analysis, confirming its effectiveness and accuracy in predicting MB adsorption. Finally, a user-friendly interface is developed to facilitate the usage of the GPR model in future applications, representing a significant advancement in environmental process modeling and ecosystem management.

Contribution to advancing aquifer geometric mapping using machine learning and deep learning techniques: a case study of the AL Haouz-Mejjate aquifer, Marrakech, Morocco

Groundwater resources in Morocco often face sustainability challenges due to increased exploitation and climate change. Specifically, the Al-Haouz-Mejjate groundwater in the Marrakesh region is faced with overexploitation and insufficient recharge. However, the complex subsurface geometries hamper hydrogeological modeling, characterization, and effective management. Reliably estimating aquifer substrate topography is critical for groundwater models but is challenged by limited direct measurements. This study develops nonlinear machine learning models to infer substrate depths by fusing sparse borehole logs with regional geospatial data. A Gaussian process regression approach provided robust holistic mapping, leveraging flexibility, and uncertainty quantification. Supplementary neural network architectures focus on isolating specific variable relationships, like surface elevation–substrate. Model accuracy exceeded 0.8 R-squared against validation boreholes. Spatial visualizations confirmed consistency across landscape transects. Elevation and piezometric data proved most predictive, though multivariate inputs were required for the lowest errors. The results highlight the power of statistical learning to extract meaningful patterns from disparate hydrological data. However, model opacity and the need for broader training datasets remain barriers. Overall, the work demonstrates advanced machine learning as a promising avenue for illuminating complex aquifer geometries essential for sustainability. Hybrid approaches that use both data-driven and physics-based methods can help solve long-standing problems with hydrogeological characterization.

A study on friction induced tribological characteristics of steel 316 L against 100 cr6 alloy under different lubricating conditions with machine learning model

The material steadily wears away from touching surfaces when two solid entities are constantly moving against one other. When more parameters and extreme materials are involved in tribological testing, then it is very difficult to analyze and observe the working phenomena. With this aim, this study uses the gaussian process regression (GPR) approach to estimate friction forces when testing SS 316 L against 100 Cr6 alloy under cryogenic and cryo + minimum amount lubrication conditions. The friction forces from ball-on test experiments were used to develop the prediction models. Then, the wear surfaces and surface morphology are analyzed under cryo and cryo+MQL conditions. The results demonstrated that the combination of MQL and CRYO cooling reduced the friction forces more than 10 times for sliding distances above ∼30 m and loads below ∼25 n. Hence, the cryo+MQL conditions are beneficial in enhancing the tribological features due to the dual cooling and lubricating effects.

Uncertainty quantification in autoencoders predictions: Applications in aerodynamics

A data-driven model is compared to classical equation-driven approaches to investigate its ability to predict quantity of interest and their uncertainty when studying airfoil aerodynamics. The focus is on autoencoders and the effect of uncertainties due to the architecture, the hyperparamaters and the choice of the training data (internal or model-form uncertainties). Comparisons with a Gaussian Process regression approach clearly illustrate the autoencoder advantage in extracting useful information on the prediction confidence even in the absence of ground truth data. Simulations accounting for internal uncertainties are also compared to the impact of the variability induced by uncertain operating conditions (external uncertainties) showing the importance of accounting for the total uncertainty when establishing prediction confidence.

Robust Gaussian process regression based on bias trimming

This paper presents a new robust Gaussian process regression (GPR) algorithm based on identifying and trimming outliers, and it can reduce the computation time and improve the accuracy compared with other robust algorithms. Currently, most existing robust GPR approaches model noise with heavy-tailed distributions that are less sensitive to outliers, such as the Laplace and Student-t distributions. However, a model that is designed this way will be analytically intractable, and the computationally expensive Bayesian approximation method needs to be adopted to obtain the posterior distribution. In our method, the deviation between normal points and outliers is modeled as a bias value, so the non-Gaussian likelihood approach, which consumes substantial time, is not necessary. Nevertheless, the decrease in calculation time is accompanied by a decrease in accuracy. To solve this problem, the trimming algorithm with an adaptive threshold is adopted to improve the prediction precision. Therefore, the proposed approach is simple but very computationally attractive. We conducted various simulation experiments to numerically evaluate the model with different outlier ratios and noise levels. We compared the approach with existing robust Gaussian process methods and other kinds of anomaly detection algorithms to demonstrate the excellent performance of the proposed method. Finally, industrial datasets are used to verify the method, and the results illustrate that it can significantly improve the practicality of the measurement system.

Gaussian process regression approach for predicting wave attenuation through rigid vegetation

Numerical modelling in the coastal environment often requires highly skilled users and can be hindered by high computation costs and time requirements. Machine Learning (ML) techniques have the potential to overcome these limitations and complement existing methods. This is an exploratory investigation utilising a Gaussian Process (GP) data-driven modelling approach that can reproduce, for the given range of conditions in this study, the results of a widely used process-based model, XBeachX, when applied to the challenging problem of wave attenuation through vegetation. This study utilises efficient sampling strategies for data exploration, providing a valuable framework for future studies. The GP model was trained on a synthetic dataset generated using the numerical model XBeachX, which was calibrated using laboratory measurements. Our findings indicate that well-trained ML models can strongly complement traditional modelling approaches, especially in an environment where data sources are increasingly available. We have also explored the underlying interactions of the GP model's input features and their relationship to the model's output through a sensitivity analysis.

A Local Gaussian Process Regression Approach to Mass Appraisal of Residential Properties

A Local Gaussian Process Regression Approach to Mass Appraisal of Residential Properties

Sustainable Urban Mobility for Road Information Discovery-Based Cloud Collaboration and Gaussian Processes

A novel cloud-based collaborative estimation framework for traffic management, utilizing a Gaussian Process Regression approach is introduced in this work. Central to addressing contemporary challenges in sustainable transportation, the framework is engineered to enhance traffic flow efficiency, reduce vehicular emissions, and support the maintenance of urban infrastructure. By leveraging real-time data from Priority Vehicles (PVs), the system optimizes road usage and condition assessments, contributing significantly to environmental sustainability in urban transport. The adoption of advanced data analysis techniques not only improves accuracy in traffic and road condition predictions but also aligns with global efforts to transition towards more eco-friendly transportation systems. This research, therefore, provides a pivotal step towards realizing efficient, sustainable urban mobility solutions.

Construction of a Mode-Combination Hamiltonian under the Grid-Based Representation for the Quantum Dynamics of OH + HO2 → O2 + H2O.

In this work, a systematic construction framework on a mode-combination Hamiltonian operator of a typical polyatomic reaction, OH + HO2 → O2 + H2O, is developed. First, a set of Jacobi coordinates are employed to construct the kinetic energy operator (KEO) through the polyspherical approach ( Phys. Rep. 2009, 484, 169). Second, due to the multiconfigurational electronic structure of this system, a non-adiabatic potential energy surface (PES) is constructed where the first singlet and triplet states are involved with spin-orbital coupling. To improve the training database, the training set of random energy data was optimized through a popular iterative optimization approach with extensive trajectories. Here, we propose an automatic trajectory method, instead of the classical trajectory on a crude PES, where the gradients are directly computed by the present ab initio calculations. Third, on the basis of the training set, the potential function is directly constructed in the canonical polyadic decomposition (CPD) form ( J. Chem. Theory Comput. 2021, 17, 2702-2713) which is helpful in propagating the nuclear wave function under the grid-based representation. To do this, the Gaussian process regression (GPR) approach for building the CPD form, called the CPD-GPR method ( J. Phys. Chem. Lett. 2022, 13, 11128-11135) is adopted where we further revise CPD-GPR by introducing the mode-combination (mc) scheme leading to the present CPD-mc-GPR approach. Constructing the full-dimension non-adiabatic Hamiltonian operator with mode combination, as test calculations, the nuclear wave function is propagated to preliminarily compute the reactive probability of OH + HO2 → O2 + H2O where the reactants are prepared in vibrational ground states and in the first triplet electronic state.

Optimization‐improved thermal–mechanical simulation of welding residual stresses in welded connections

AbstractThis paper presents a novel computer‐aided computational framework to determine the optimum shape parameters in a welding heat source model using a coupled supervised Gaussian process regression (GPR) and genetic algorithm (GA) approach in estimating the welding residual stresses. The experimental X‐ray diffraction (XRD) approach validates the optimization‐improved thermal–mechanical simulation method. The validation of the proposed approach includes the welded plates with simple geometry to welded pipe‐to‐plate and the circular hollow section joints with complex topologies. The optimization‐derived shape parameters in a welding heat source model lead to close estimates of the temperature history and the welding residual stresses for these types of welded joints considered in this study.

Modeling the interest rates term structure using Machine Learning: a Gaussian process regression approach

The correct modeling of the interest rates term structure should definitely be considered an aspect of primary importance since the forward rates and the discount factors used in any financial and risk analysis are calculated from such structure. The turbulence of the markets in recent years, with negative interest rates followed by their recent substantial rise, the period of the COVID pandemic crisis, the political instabilities linked to the war between Ukraine and Russia have very often led to observe anomalies in the shape of the interest rate curve that are difficult to represent using traditional econometric models, to the point that researchers have to address this modeling problem using Machine Learning methodologies. The purpose of this study is to design a model selection heuristic which, starting from the traditional ones (Nelson-Siegel, Svensson and de Rezende-Ferreira) up to the Gaussian Process (GP) Regression, is able to define the best representation for a generic term structure. This approach has been tested over the past five years on term structures denominated in five different currencies: the Swiss Franc (CHF), the Euro (EUR), the British Pound (GBP), the Japanese Yen (JPY) and the U.S. Dollar (USD).

Improved Quantum-Classical Treatment of N2-N2 Inelastic Collisions: Effect of the Potentials and Complete Rate Coefficient Data Sets.

In this study, complete (i.e., including all vibrational quantum numbers in an N2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N2-N2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100-9000 K. To reach this goal, we improved a mixed quantum-classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique (i.e., the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.

Analytical fragility relation for buried cast iron pipelines with lead-caulked joints based on machine learning algorithms

A new numerical-based fragility relation for cast iron (CI) pipelines with lead-caulked joints subjected to seismic body-wave propagation is proposed in this article. Two-dimensional 1600-m-length finite element models for pipelines buried in sand are developed in OpenSees. Parametric analysis is performed to investigate the influence of various parameters on the damage estimates of the buried pipelines. Numerical analyses are conducted to estimate the repair rates ( RR) for CI pipelines subjected to wave propagation. The predictive model for RR is thus developed based on the numerical results and the Gaussian Process Regression approach. The model developed employs four predictor variables, namely, the peak particle velocity and wave propagation velocity along axial direction, the maximum soil shear force per unit length, and the outer diameter of pipelines, exhibiting desirable performance in terms of predictive efficiency and generalization. The performance of the developed relation is compared to several existing fragility relations. The new fragility relation can be used to estimate RR for CI pipelines with lead-caulked joints with outer diameters ranging from 169 to 1554 mm subjected to seismic body-wave propagation.

Evaluation and Prediction of Blast-Induced Ground Vibrations: A Gaussian Process Regression (GPR) Approach

Ground vibration is one of the most hazardous outcomes of blasting. It has a negative impact both on the environment and the human population near to the blasting area. To evaluate the magnitude of blasting vibrations, it is important to consider PPV as a fundamental critical base parameter practice in terms of vibration velocity. This study aims to explore the application of different soft computing techniques, including a Gaussian process regression (GPR), decision tree (DT), and support vector regression (SVR), for the prediction of blast-induced ground vibration (PPV) in quarry mining. The three models were evaluated using classical mathematical evaluation metrics (R2, RMSE, MSE, MAE). The result shows that the GPR model achieves an excellent prediction result; with R2 = 0.94, RMSE = 0.0384, MSE = 0.0014, and MAE = 0.0265, it shows high accuracy in predicting PPV. The Shapley additive explanation (SHAP) results emphasize the importance of understanding the interactions between the various factors and their effects on the vibration assessment. The findings can inform the development of more sustainable and environmentally friendly models for predicting blasting vibrations. Using a GPR to simulate and predict blasting-induced ground vibrations is the study’s main contribution. The GPR can capture complicated, non-linear correlations in data, making it ideal for blast-induced ground vibrations, which are dynamic and nonlinear. By using a Gaussian process regression, we can help companies and researchers improve the safety and efficiency in blast-induced ground vibration environments.

Probabilistic prediction of uniaxial compressive strength for rocks from sparse data using Bayesian Gaussian process regression with Synthetic Minority Oversampling Technique (SMOTE)

Uniaxial compressive strength (UCS) of rocks is one of key rock strength parameters. Generally speaking, UCS can be measured directly through uniaxial compression tests, which is often unfeasible, especially when intact rock samples are highly fragile. Alternatively, the UCS of rocks can be estimated indirectly from other easily available rock indices. Note that adequate measurement data is the prerequisite for the accurate estimation of UCS using indirect methods. This may be difficult to achieve due to the limitation of time and budget, especially for small- to medium-sized projects. In this case, it becomes a challenging issue on how to develop a robust and reliable model for UCS estimation using the sparse measurement data. A fully Bayesian Gaussian process regression (fB-GPR) approach with Synthetic Minority Oversampling Technique (SMOTE) is proposed in this paper to address this problem. A real-life example from Malaysia was used for illustration and validation of proposed method. Results showed that when the synthetic sample size in SMOTE reaches 30 (i.e., optimal synthetic sample size), the coefficient of determination (R2) increases by about 18.92%, and the accuracy of feature selection reaches 98%, compared with the scenario with only sparse measurement data used for fB-GPR model development.

Monthly sodium adsorption ratio forecasting in rivers using a dual interpretable glass-box complementary intelligent system: Hybridization of ensemble TVF-EMD-VMD, Boruta-SHAP, and eXplainable GPR

The sodium adsorption ratio (SAR) is the most crucial irrigation water quality indicator to diagnose the suitability of agricultural water resources. Due to this reason, accurate forecasting of SAR in the absence of its time series, based on limited input sequences, is recently considered a challenging environmental issue on a monthly scale. This research developed a dual eXplainable multivariate expert framework for the first time to forecast monthly SAR at Zayanderud River, Iran. The framework (i.e., BS-GPR-E.TVF-EMD-VMD) consisting of a Boruta coupled with SHapley Additive exPlanations (Boruta-SHAP) feature selection, an ensemble of time-varying filter-based empirical mode decomposition (TVF-EMD) and variational modal decomposition (VMD), namely (E.TVF-EMD-VMD), and eXplainable Gaussian process regression (GPR). The main novelty of this framework is converting the “black-box” nature of the forecasting model to a dual interpretable “glass box” before and during the learning process. For this purpose, among nine hydrometric and water quality parameters associated with Zayanderud River at two stations (Regulating dam and Zaman Khan) over the period of 1969 to 2016, the significant two-month antecedent information (lags) signals were extracted using the Boruta-SHAP feature selection. Afterwards, the optimal inputs signal lags for each station were decomposed into sub-components to reduce the complexity and non-stationary of original signals using three pre-processing techniques (i.e., E.TVF-EMD-VMD, TVF-EMD, and VMD). The decomposed predictors were employed as inputs into the multilayer perceptron neural network (MLP), Random Forest (RF), Elman recurrent neural network (ERNN), and eXplainable GPR approaches. Statistical validation and infographic tools revealed that the BS-GPR-E.TVF-EMD-VMD regarding the best performance in the Regulating dam (R = 0.9817, RMSE = 0.1431, and NSE = 0.8866) and Zaman Khan (R = 0.9632, RMSE = 0.0610, and NSE = 0.9233) stations, outperformed the other complementary and standalone counterpart frameworks followed by the BS-GPR-TVF-EMD and BS-ERNN-E.TVF-EMD-VMD, respectively. SHAP explainer through the GPR model clearly interpreted the effect of the lagged-time sub-components related to each predictor and represented the impact of each decomposition technique on the input signals through E.TVF-EMD-VMD aiming to forecast SAR in standalone and complementary frameworks.

Modeling the perceptions of Rumbling, humming and booming in the context of vehicle interior sounds

Sensations associated with an auditory perception of low-frequency tonal components are humming, rumbling and booming. While humming is commonly associated with an audible low-frequency tone, rumbling requires a temporal level fluctuation of such a tonal component and booming is associated with sounds that, in addition to the low-frequency tone, contain higher tonal components, which are related to the low-frequency tone. This study presents a model that predicts the magnitude of these sensations for interior sounds of vehicles with combustion engines running at low rotation rates, where low-frequency components are often audible. For the model development, own experimental data of recorded interior sounds and altered versions of these sounds were used. The model combines an auditory processing model with a Gaussian Process Regression approach. Key features of the auditory processing model are that it simulates the frequency-place transformation at the auditory periphery with a bank of auditory band pass filters and the frequency selectivity to temporal amplitude modulations with a bank of modulation band pass filters. It is shown that auditory filters up to a center frequency of 1000 Hz and modulation filters of up to 28 Hz are required for a good prediction of the data.

Comprehensive modeling of frictional pressure drop during carbon dioxide two-phase flow inside channels using intelligent and conventional methods

Environmentally friendly nature of CO2, associated with its safety and high efficiency, has made it a widely used working fluid in heat exchangers. Since CO2 has strange thermophysical features, specific models are required to estimate its two-phase characteristics, particularly frictional pressure drop (FPD). Herein, a widespread dataset, comprising 1195 experimental samples for two-phase FPD of CO2 was adopted from 10 sources to fulfill this requirement. The literature correlations failed to provide satisfactory precisions and exhibited the average absolute relative errors (AAREs) between 29.29% and 67.69% from the analyzed data. By inspiring the theoretical method of Lockhart and Martinelli, three intelligent FPD models were presented, among which the Gaussian process regression approach surpassed the others with AARE and R2 values of 5.48% and 98.80%, respectively in the test stage. A novel simple correlation was also derived based on the least square fitting method, which yielded opportune predictions with AARE of 19.76% for all data. The truthfulness of the newly proposed models was assessed through a variety of statistical and visual analyses, and the results affirmed their high reliability over a broad range of conditions, channel sizes and flow patterns. Furthermore, the novel models performed favorably in describing the physical attitudes corresponding to two-phase FPD of CO2. Eventually, the importance of operating factors in controlling the FPD was discussed through a sensitivity analysis.

A hybrid framework for predicting the remaining useful life of battery using Gaussian process regression

The battery will inevitably deteriorate in its service life. Therefore, accurate prediction of the remaining useful life (RUL) is critical to the durability of the battery energy storage systems (ESS). The RUL prediction framework of Gaussian process regression(GPR) based on automatic stack autoencoder (SAE) and improved whale optimization algorithm (WOA) is proposed in this research paper. Firstly, the SAE and gray relation analysis are proposed to extract indirect health indicators (HIs) from battery degradation data. Secondly, the Gaussian process regression (GPR) approach combined with the WOA method to establish the RUL prediction framework. Besides, aiming at the disadvantage that WOA is prone to fall into local optimization, the WOA based on the sine cosine algorithm of decentralized foraging strategy is proposed to optimize the prediction ability of the GPR. Finally, compared with the prediction results of existing approaches under the same conditions, the simulation results indicate that the RUL prediction errors based on the proposed algorithm are controlled within 2 %, which has good advantages and prediction ability.