Gaussian Process Regression Model Research Articles

Surrogate modeling with non-stationary-noise based Gaussian process regression and K-Fold ANN for systems featuring uneven sensitivity distribution

In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26 % and 22 % less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25 % greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions.

Thermophysical properties and enhancement behavior of novel B4C-nanoadditive RT35HC nanocomposite phase change materials: Structural, morphological, thermal energy storage and thermal stability

This study aims to enhancement the thermal conductivity of RT35HC, as a commercial paraffin, by integrating boron carbide (B4C) nanoparticles for the first time, thereby producing B4C-nanoadditive nanocomposite PCMs. The B4C nanoparticles were reinforcement to RT35HC at mass fraction percentages (wt.%) of 0.5, 1, 1.5 and 2 by melting and physical mixing method. The structural and morphological characteristics of both pure and nanocomposite PCMs were examined using XRD, FT-IR, FE-SEM, and EDX. Thermal properties were investigated through DSC, TGA/DTA, and thermal conductivity measurements using the KD2-Pro device. The Gaussian process regression (GPR) model was used to analyze the Cp values in relation to temperature and additive ratio. Structural and morphological analysis results indicated a homogeneous distribution of nanoparticles within the PCM matrix, without any significant chemical or physical alterations. The introduction of B4C-nanoadditive did not markedly affect the melting and solidification temperatures. However, melting and solidification enthalpies decreased proportionally with increased nanoadditive ratios, with the greatest reductions being 7.44 % and 5.74 % at a 2 wt% nanoaddition rate, respectively. As the nanoadditive ratio increased, the thermal conductivity (k) and specific heat capacity (Cp) of RT35HC in both solid and liquid-phases enhanced significantly. Specifically, solid-phase (25 °C) k values increased by 67.51 % from 0.197 to 0.33, and liquid-phase (50 °C) k values by 15.29 % from 0.170 to 0.196. The highest Cp values in the solid and liquid-phases were measured as 3.01 and 2.49, respectively, in the nanocomposite with a high nanoadditive ratio. The GPR method yielded a success rate of 0.9015. Additionally, the nanocomposites exhibited enhanced thermal stability and higher thermal decomposition temperatures. Based on these characterizations, the fabricated B4C-nanoadditive nanocomposite PCMs show promise for application in TES and TM systems.

Machine-Learning-Based Kinetic-Free Hybrid Gray-Box Model to Predict Sulfuric-Acid-Catalyzed Esterification Reaction.

The sulfuric-acid-catalyzed esterification reaction of 2-butanol and propionic anhydride is a vital industrial process. In this paper, several experiments are conducted via reaction calorimetry to validate that both sulfuric and propionic acids have discernible catalytic effects on the reaction. This finding complicates the accurate description of the reaction kinetics through traditional methods. So this paper turns to a kinetic-free black-box model, Gaussian process regression (GPR) model via 24 experiments, as a more adaptable approach. Besides, the best GPR model is combined with traditional heat balance model to generate a hybrid gray-box model, which can give complete knowledge of reaction process. The hybrid gray-box model finally achieves maximum root-mean-square error (RMSE) of 0.0069 for conversion, 0.6535 for temperature, and 10.6087 for heat flow rate, underscoring its pretty good predictive ability.

A physical simulation-machine learning model for optimal process schemes in laser-based directed energy deposition process

The major challenge faced is the definition of optimal process variables for rich quality of fabricated parts in laser-based directed energy deposition (DED-LB) processes. However, predicting the optimal process scheme using machine learning models is still challenging owing to the need for a large amount of training experimental data with high costs in DED-LB. In view of this, a physical simulation (PS)-machine learning (ML) model using a relatively small accurate data set of 31 simulation data for optimal process schemes is proposed in DED-LB process in this study. Firstly, a powder-scale high precision phenomenon model incorporating the mass transfer, phase transformations and heat transfer and using Lagrangian particle model to add mass is developed to depict the DED-LB process. Then, a Gaussian process regression (GPR) agent model is established to rapidly and accurately predict the geometry and dilution rate of deposition tracks under different manufacturing parameters based on the high precision simulation results. Finally, a PS-ML model for process parameter optimization is developed using the particle swarm algorithm (PSO), and the optimized parameters are experimentally validated. The results show that the developed powder-scale model and GPR model results are consistent with the Inconel 718 alloy experimental results. The proposed PS-ML model can increase the accuracy of the ML models even with a small simulation data set. None of PS-ML model optimization results has a relative error of more than 3% to the experimental results, and the dilution rate is reduced by up to 61.66% compared to the experimental design parameters without optimization. The proposed physical simulation-machine learning model in this study enables inexpensive and accurate optimization of DED-LB process parameters.

A novel decoupled approach combining invertible cross-entropy method with Gaussian process modeling for reliability-based design and topology optimization

Design optimization considering the presence of uncertainties in parameters poses an extremely challenging problem. The source of difficulties comes with reliability-based formulations, where addressing the probabilistic problem exhausts the large computing efforts for failure estimations of the structure violating limit-state functions (LSFs). This paper proposes a novel decoupled approach for effectively solving reliability-based design optimization (RBDO) problems, namely an invertible cross-entropy (iCE) method advantageously combined with a Gaussian process regression (GPR) model, termed as iCE-GPR. The GPR model is applied to approximate the spectrum of LSFs under random parameters. Furthermore, to enhance the accurate prediction of the system failure probability, an active learning process is applied to systematically refine the GPR model by adding new learning points in the region with the largest uncertainty and high-reliability sensitivity through the maximization of an expected feasibility function (EFF). Based on the updated GPR model, the failure probability is estimated by a cost-effective cross-entropy (CE) method without any calls to the actual performance function. To perform the decoupling optimization process with the reliability analysis, the novel iCE, based on the CE method, is developed to update the most probable point (MPP) assigned for the next deterministic optimization process in determining the new optimal design. The method iteratively performs the deterministic optimization process based on the MPP underpinning LSFs sequentially updated by the active learning process. The proposed iCE-GPR method fast-converges the optimal design and significantly alleviates computational burdens associated with reliability analyses. The proposed method is also applied to solve a reliability-based topology optimization (RBTO) problem. Four numerical examples for both the RBDO and RBTO problems are provided to illustrate efficiency and robustness of the proposed iCE-GPR method.

Hyper‐parameter optimized GPR model based on chaos game algorithm for RF power transistors

AbstractIn this paper, a new frequency domain behavior model for radio frequency (RF) power transistors based on a hyper‐parameter optimized Gaussian process regression (GPR) method is presented. The chaos game optimization (CGO) algorithm is used to optimize GPR hyperparameters, resulting in the CGO‐GPR model. The basic theory as well as the details of the modeling process are presented. Validation of the model is conducted using a 10‐watt GaN power transistor. Compared to the standard GPR model, the proposed model achieved a significant improvement. Furthermore, the comparison with the particle swarm optimization (PSO) based GPR model (PSO‐GPR) showed that the proposed model allows achieving superior performance, thereby confirming the effectiveness of the developed modeling technique.

Adaptive switching and routing protocol design and optimization in internet of things based on probabilistic models

Through smart cities, Intelligent Transportation Systems (ITS), the agricultural sector, and wearable devices, the Internet of Things (IoT) has revolutionized several human interests. Through the development of new cluster tasks, the Decision-Making System (DMS) of Cluster Heads (CHs), and improving the accuracy of traffic prediction and reliability of transportation, the present study intends to improve the energy depletion of IoT devices. The paper explores the subject of data flow optimization using Fuzzy Assisted Cuckoo Search Optimization (FACSO), traffic flow using Gaussian Process Regression (GPR), and CH prediction using the Stochastic Optimization Algorithm (SOA). Optimizing network lifetime while minimizing Energy Consumption (EC) is feasible through the practical application of the SOA, GPR, and FACSO models. Increasing End-to-End Delay (EED), Network Throughput (NT), and energy efficiency can be rendered feasible through a real-time DMS regarding routing employing a novel approach referred to as FACSO. This approach has enhanced the efficacy and reliability of Wireless Sensor Networks (WSN). With up to 500 nodes and an EC of 0.3451 J, the experiment's findings demonstrate that a proposed SOA-FACSO model achieves superior EED.

USING MACHINE LEARNING TO PREDICT THE MECHANICAL PROPERTIES OF PET FIBER-REINFORCED CONCRETE

Fiber-reinforced concrete enhances structural integrity by improving post-cracking behavior and ductility, yet traditional fibers can be costly and have a significant environmental impact. Recently, polyethylene terephthalate (PET) fiber, derived from recycled plastic bottles, has been used as a reinforcing material in concrete to enhance its mechanical properties. Utilizing advanced machine learning algorithms, this research analyzes a comprehensive dataset collected from existing literature on the mechanical properties of PET fiber-reinforced concrete (PFRC), including concrete density, water-to-binder ratio, fine and coarse aggregates, and fiber parameters such as volume fraction and aspect ratio of PET fibers. Through the application of Polynomial Regression, Exponential Gaussian Process Regression (GPR), and Cubic Support Vector Machine (SVM) models, the study effectively predicts PFRC’s mechanical behavior, showcasing high R² values indicating the models’ predictive strength: 0.93 for compressive, 0.92 for flexural, and 0.92 for tensile properties. This investigation highlights the exceptional accuracy of Exponential GPR and Cubic SVM models in capturing complex, non-linear relationships within the material, demonstrating machine learning’s capability to advance the sustainable development of construction materials. This study provides significant insights into optimizing the use of recycled fibers for concrete reinforcement.

USING MACHINE LEARNING TO PREDICT THE MECHANICAL PROPERTIES OF PET FIBER-REINFORCED CONCRETE

Fiber-reinforced concrete enhances structural integrity by improving post-cracking behavior and ductility, yet traditional fibers can be costly and have a significant environmental impact. Recently, polyethylene terephthalate (PET) fiber, derived from recycled plastic bottles, has been used as a reinforcing material in concrete to enhance its mechanical properties. Utilizing advanced machine learning algorithms, this research analyzes a comprehensive dataset collected from existing literature on the mechanical properties of PET fiber-reinforced concrete (PFRC), including concrete density, water-to-binder ratio, fine and coarse aggregates, and fiber parameters such as volume fraction and aspect ratio of PET fibers. Through the application of Polynomial Regression, Exponential Gaussian Process Regression (GPR), and Cubic Support Vector Machine (SVM) models, the study effectively predicts PFRC’s mechanical behavior, showcasing high R² values indicating the models’ predictive strength: 0.93 for compressive, 0.92 for flexural, and 0.92 for tensile properties. This investigation highlights the exceptional accuracy of Exponential GPR and Cubic SVM models in capturing complex, non-linear relationships within the material, demonstrating machine learning’s capability to advance the sustainable development of construction materials. This study provides significant insights into optimizing the use of recycled fibers for concrete reinforcement.

Prediction of key quality attributes in Salvia miltiorrhiza standard decoction using a Gaussian process regression model.

Nonstationary, nonlinear mass transfer in traditional Chinese medicine (TCM) extraction poses challenges to correlating process characteristics with quality parameters, particularly in defining clear parameter ranges for the process. The aim of the study was to provide a solution for quality consistency analysis in TCM preparation processes. Salvia miltiorrhiza was taken as an example for 15 batches of standard decoction. Using aqueous extract, alcoholic extract, and the content of salvianolic acid B as herb material key quality attributes, multiple nonlinear regression, Gaussian process regression, and artificial neural network models were employed to predict the key quality attributes including the paste yield, the content of salvianolic acid B, and the transfer rate. The evaluation criteria were root mean square error, mean absolute percentage error, and R2. The Gaussian process regression model had the best prediction effect on the paste yield, the content of salvianolic acid B, and the transfer rate, with R2 being 0.918, 0.934, and 0.919, respectively. Utilizing Gaussian process regression model confidence intervals, along with Shewhart control and intervals optimized through process capability index analysis, the quality control range of the standard decoction was determined as follows: paste yield, 25.14%-33.19%; salvianolic acid B content, 2.62%-4.78%; and transfer rate, 56.88%-64.80%. This study combined the preparation process of standard decoction with the Gaussian process regression model, accurately predicted the key quality attributes, and determined the quality parameter range by using process analysis tools, providing a new idea for the quality consistency standard of TCMprocesses.

Post-earthquake building damage assessment: A multi-period inspection routing approach for Gaussian process regression

In the wake of seismic events, prompt and accurate building damage assessment is crucial to inform post-disaster interventions and recovery efforts. This paper advances a novel multi-period planning strategy for post-earthquake building inspections, conceptualizing the task as a multi-period orienteering problem (MPOP). In this framework, each building selected for inspection hosts a specific reward indicating its informative value for damage assessment. The objective is to design inspection routes that maximize damage information acquisition while adhering to time constraints. After data collection, we utilize a Gaussian process regression (GPR) model to estimate the damage in uninspected buildings. To validate our approach, we conduct an earthquake simulation with realistic building information from San Francisco. The experimental outcomes reveal that our multi-period damage assessment framework maintains robust performance across diverse scenarios and consistently surpasses conventional period-by-period inspection strategies, yielding enhanced damage information acquisition and greater precision in damage estimation. This outcome underscores the effectiveness of our proposed method in strengthening post-earthquake damage assessment and improving recovery planning.

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.

Development of an Emulator for Radiation Physics Simulator Using Stochastic Variational Gaussian Process Model

This paper describes an emulator that uses a Stochastic Variational Gaussian process (SVGP) regression model to parameterize radiation in a numerical weather prediction (NWP) model that meteorologically models the Earth's weather system. The computation of radiative processes is very large, accounting for most of the total NWP model computation. Statistical emulators are surrogate models that represent simulators and can overcome the computational limitations of very complex simulators such as radiative processes. Recently, artificial neural network-based radiative transfer emulators have been developed, and in this study, a statistical model, GP, is used to develop a radiative transfer emulator. The GP model has the advantage of calculating the uncertainty of the prediction along with the prediction, so the uncertainty of the prediction can be utilized appropriately. However, the computational complexity of the conventional GP model is very high, making it difficult to apply to large data. To solve this problem, an approximate approach, the SVGP model, was utilized. To further reduce the dimensionality of the input variables, we used a combined neural network and SVGP model. As a result, the SVGP-based radiative physics emulator improved its accuracy by about 20% compared to the artificial neural network emulator. However, the computation speed was about 3 to 9 times slower than the neural network emulator, but it was faster than the computation speed of the NWP model. This suggests that statistical emulators can be used to replace NWP model simulators.

Complementing Drawability Assessment of Deep-Drawn Components With Surrogate-Based Global Sensitivity Analysis

Abstract In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions. Complementing this process with a global sensitivity analysis (GSA) can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component. Here, we show in an exemplary application problem, that both a standard Gaussian process regression (GPR) model and an ensemble model can provide commendable results at a fraction of the computational cost. We compare our surrogate models to existing approaches in the field. Furthermore, by comparing drawability measures we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.

Machine learning-powered estimation of malachite green photocatalytic degradation with NML-BiFeO3 composites

This study explores the potential of photocatalytic degradation using novel NML-BiFeO3 (noble metal-incorporated bismuth ferrite) compounds for eliminating malachite green (MG) dye from wastewater. The effectiveness of various Gaussian process regression (GPR) models in predicting MG degradation is investigated. Four GPR models (Matern, Exponential, Squared Exponential, and Rational Quadratic) were employed to analyze a dataset of 1200 observations encompassing various experimental conditions. The models have considered ten input variables, including catalyst properties, solution characteristics, and operational parameters. The Exponential kernel-based GPR model achieved the best performance, with a near-perfect R2 value of 1.0, indicating exceptional accuracy in predicting MG degradation. Sensitivity analysis revealed process time as the most critical factor influencing MG degradation, followed by pore volume, catalyst loading, light intensity, catalyst type, pH, anion type, surface area, and humic acid concentration. This highlights the complex interplay between these factors in the degradation process. The reliability of the models was confirmed by outlier detection using William’s plot, demonstrating a minimal number of outliers (66–71 data points depending on the model). This indicates the robustness of the data utilized for model development. This study suggests that NML-BiFeO3 composites hold promise for wastewater treatment and that GPR models, particularly Matern-GPR, offer a powerful tool for predicting MG degradation. Identifying fundamental catalyst properties can expedite the application of NML-BiFeO3, leading to optimized wastewater treatment processes. Overall, this study provides valuable insights into using NML-BiFeO3 compounds and machine learning for efficient MG removal from wastewater.

A deterministic and probabilistic hybrid model for wind power forecasting based improved feature screening and optimal Gaussian mixed kernel function

Forecasting wind power is crucial to ensuring the electricity system runs steadily. However, wind power forecasting is hampered by the randomness and volatility of wind power data. In this paper, a deterministic and probabilistic decomposition ensemble model based on improved feature screening and optimal Gaussian mixed kernel function is proposed, which mainly includes feature screening, feature learning, intelligent weighted integration and interval prediction modules. First, an improved feature screening (IFS) is proposed to capture the optimal features of the original wind power data, eliminating the interference of redundant features. Then an optimized deep neural network is suggested to learn the outcomes of IFS and further explore the temporal correlation of these features. Then, considering the difference of the contribution of each feature component, the final result is obtained by integrating the preliminary forecast results using intelligent weighted integration (IWI). Finally, an optimal mixed kernel-based Gaussian process regression model is developed for interval prediction, which improves the adaptability of the model. The data sets of two wind farms in Inner Mongolia were used for empirical testing. On the two datasets, the model's root mean square error (RMSE) is 1.1845 and 1.7354, respectively, both of which are lower than the comparison model. The model has the lowest coverage width criterion (CWC) of 0.1499 and 0.1460 on the two datasets, respectively.

Application of an active learning method for cumulative fatigue damage assessment of floating wind turbine mooring lines

Long-term cumulative fatigue damage of mooring lines is crucial for the design of floating wind turbine structures (FWTs). Although many efforts are carried out for the offshore floating platforms, there still needs to be an efficient approach for assessing the long-term fatigue damage of the floating wind turbine mooring lines due to the complex loading in FWTs. An active learning approach named AK-DA (Adaptive Kriging Damage Assessment) was recently proposed for the cumulative fatigue damage assessment of wind turbine structures. However, in the original work, the AK-DA approach was only tested on fatigue damage assessment of a 5MW wind turbine tower with monopile support structures. It is unclear whether it is applicable to other parts of the wind turbine system, especially considering the complex loading of FWTs. Therefore, in this work, the AK-DA approach is used to assess the cumulative fatigue damage of mooring lines. The Gaussian process regression (Kriging) model is used to predict the fatigue damage of the mooring line under different wind-wave cases. The cumulative fatigue damage of the mooring lines in the IEA 15MW semi-submersible wind turbines is assessed with the AK-DA approach. The numerical simulation results show that the AK-DA approach can efficiently and accurately estimate the cumulative fatigue damage of the mooring lines. Compared to the traditional simulation approach, the AK-DA approach can increase efficiency by more than 45 times, and the absolute error is less than 1%. This active learning approach could serve as a helpful tool for offshore mooring system designers, facilitating the cumulative fatigue damage assessment during the design process.

Inversion of soil carbon, nitrogen, and phosphorus in the Yellow River Wetland of Shaanxi Province using field in situ hyperspectroscopy

Soil nitrogen and phosphorus are directly related to soil quality and vegetation growth and are, therefore, a common research topic in studies on global climate change, material cycling, and information exchange in terrestrial ecosystems. However, collecting soil hyperspectral data under in situ conditions and predicting soil properties, which can effectively save time, manpower, material resources, and financial costs, have been generally undervalued. Recent optimization techniques have, however, addressed several of the limitations previously restricting this technique. In this study, hyperspectral data were taken from surface soils under different vegetation types in the wetlands of the Shaanxi Yellow River Wetland Provincial Nature Reserve. Through in situ original and first-order differential transformation spectral data, three prediction models for soil carbon, nitrogen, and phosphorus contents were established: partial least squares (PLSR), random forest (RF), and Gaussian process regression (GPR). The R2 and RMSR of the constructed models were then compared to select the optimal model for evaluating soil content. The soil organic carbon, total nitrogen, and total phosphorus content models established based on the first-order differential had a higher accuracy when modeling and during model validation than those of other models. Moreover, the PLSR model based on the original spectrum and the Gaussian process regression model had a superior inversion performance. These results provide solid theoretical and technical support for developing the optimal model for the quantitative inversion of wetland surface soil carbon, nitrogen, and phosphorus based on in situ hyperspectral technology.

Machine learning predictions for carbon monoxide levels in urban environments

The increasing carbon emissions in Malaysia necessitate accurate methods to track and control pollution levels. This study focuses on predicting carbon monoxide (CO) concentrations in Petaling Jaya using various machine learning models, and two important parameters, CO concentration and time, were considered in the analysis. Six distinct machine learning models were assessed to gauge their predictive capabilities. These models encompassed a range of regression modeling techniques namely; Linear, Tree, Gaussian Process, Ensemble of Trees, Support Vector, and Artificial Neural Networks (ANN) modelling. The Matern 5/2 Gaussian Process Regression (GPR) model consistently outperformed other models across all scenarios, demonstrating high R2 values and low RMSE, MSE, and MAE values. Specifically, in scenarios 1, 2, 3, and 4, the Matern 5/2 model exhibited the lowest RMSE (0.084–0.088) and highest R2 (0.97), highlighting its reliability and robustness in predicting CO concentrations. Additionally, the Rational Quadratic model achieved an R2 of 0.97 with an RMSE of 0.088 in scenario 1, while the Quadratic SVM excelled in scenario 3 with an R2 of 0.965 and low RMSE, MSE, and MAE values (0.085, 0.007, and 0.066). These findings provide valuable insights for environmental protection, renewable energy transition, energy efficiency, sustainable land use planning, and public awareness. However, acknowledging the study's single-area focus and potential limitations in representing diverse regions, further research is warranted to explore carbon emissions across varied areas and enhance the generalizability of the findings.

Machine Learning-Assisted design of boron and nitrogen doped graphene nanosheets with tailored thermomechanical properties

Doping graphene with boron and/or nitrogen enhances its potential for various applications, such as electronics and energy devices. However, these modifications impact the material's properties, influencing its response to external forces, temperature, and heating. Investigating the connection between the structure of co-doped graphene nanosheets and their thermomechanical properties is crucial for accurate predictions and tailored nanosheet engineering. In the present study, molecular dynamics (MD) simulations were performed to compute the thermal and mechanical properties of 300 randomly generated boron/nitrogen co-doped graphene nanosheets with doping concentrations in the range of 0%-15%. Next, the obtained MD results were used to train, tune, and validate a wide spectrum of supervised machine learning models, including linear regression models, regression trees, support vector machines, Gaussian process regression models, kernel approximation models, ensembles of regression trees, and regression neural networks. Our aim is to find models that better estimate, without overfitting, the structure-properties relation of boron/nitrogen co-doped nanosheets. To this end, the models with the highest coefficient of determination (R2) and the lowest root mean square error (RMSE) were utilized. Finally, an appropriate implementation of guided random search algorithms, mainly Genetic Algorithms, was used to solve the inverse problem, i.e., find the nanosheet structure which exhibits the desired set of property values. To this end, thermal conductivity, Young’s modulus, failure stress, and failure strain were specified as target values. A detailed comparison between the employed models and their validation via MD simulations is also included. The achieved results provide sufficient evidence of the accuracy and viability of the applied procedure in both prediction of thermomechanical properties as well as identification of structures with desired properties. This study provides a roadmap that could help scientists and engineers develop nanosheets-based materials with tunable thermomechanical properties, ultimately leading to the creation of innovative and high-performance technologies.