Levenberg-Marquardt Backpropagation Research Articles

Performance Analysis of Cooperative Spectrum Sensing using Empirical Mode Decomposition and Artificial Neural Network in Wireless Regional Area Network

Background: Radio spectrum is natural and the most precious means in wireless communication systems. Optimal spectrum utilization is a key concern for today's cutting-edge wireless communication networks. The impending problem of the lack of available spectrum has prompted the development of a new idea called “Cognitive Radio” (CR). Cooperative spectrum sensing (CSS) is utilized to improve the detection performance of the system. Several fusion algorithms of decision-making are proposed for sensing the licensed user, but they do not work well under low signal-to-noise ratio (SNR). Objectives: To address the issue of poor detection performance under low SNR, Empirical mode decomposition (EMD) and artificial neural network (ANN) based CSS under Rayleigh multipath fading channel in IEEE 802.22 wireless regional area network (WRAN) is proposed in this paper. Method: In this work, we propose the use of ANN as a fusion center. First, the received signal's energy is calculated using EMD. The computed energy, SNR, and false alarm probability are combined to form a data set of 2048 samples. They are utilized to train Levenberg- Marquardt back propagation training algorithm-based feed-forward neural network (FFNN). Using this trained network, CSS in WRAN is simulated under Rayleigh multipath fading. Results: Simulation results show that the proposed CSS method based on EMD-ANN outperforms the standard fast Fourier transform (FFT) and EMD detection-based cooperative spectrum sensing with a hard "OR" fusion at low SNR. With Pf =0.01, 100% detection accuracy with proposed techniques is obtained at SNR= -22dB. Conclusion: The findings show that the suggested approach outperforms EMD and FFT based energy detection scheme-based traditional CSS in low SNR environments.

Innovative thermal management in the presence of ferromagnetic hybrid nanoparticles

In the present work, a simple intelligence-based computation of artificial neural networks with the Levenberg-Marquardt backpropagation algorithm is developed to analyze the new ferromagnetic hybrid nanofluid flow model in the presence of a magnetic dipole within the context of flow over a stretching sheet. A combination of cobalt and iron (III) oxide (Co-Fe2O3) is strategically selected as ferromagnetic hybrid nanoparticles within the base fluid, water. The initial representation of the developed ferromagnetic hybrid nanofluid flow model, which is a system of highly nonlinear partial differential equations, is transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The reference data set of the possible outcomes is obtained from bvp4c for varying the parameters of the ferromagnetic hybrid nanofluid flow model. The estimated solutions of the proposed model are described during the testing, training, and validation phases of the backpropagated neural network. The performance evaluation and comparative study of the algorithm are carried out by regression analysis, error histograms, function fitting graphs, and mean squared error results. The findings of our study analyze the increasing effect of the ferrohydrodynamic interaction parameter β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} to enhance the temperature and velocity profiles, while increasing the thermal relaxation parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} decreases the temperature profile. The performance on MSE was shown for the temperature and velocity profiles of the developed model about 9.1703e−10, 7.1313ee−10, 3.1462e−10, and 4.8747e−10. The accuracy of the artificial neural networks with the Levenberg-Marquardt algorithm method is confirmed through various analyses and comparative results with the reference data. The purpose of this study is to enhance understanding of ferromagnetic hybrid nanofluid flow models using artificial neural networks with the Levenberg-Marquardt algorithm, offering precise analysis of key parameter effects on temperature and velocity profiles. Future studies will provide novel soft computing methods that leverage artificial neural networks to effectively solve problems in fluid mechanics and expand to engineering applications, improving their usefulness in tackling real-world problems.

A neural network computational procedure for the novel designed singular fifth order nonlinear system of multi-pantograph differential equations

The current investigations present the numerical solutions of the novel singular nonlinear fifth-order (SNFO) system of multi-pantograph differential model (SMPDM), i.e., SNFO–SMPDM. The novel SNFO–SMPDM is obtained using the sense of the second kind of typical Emden–Fowler and prediction differential models. The features of shape factor, pantograph along with singular points are provided for all four obtained classes of the SNFO–SMPDM. The extensive use of the singular models is observed in the engineering and mathematical systems, e.g., inverse systems and viscoelasticity or creep systems. For the correctness of the proposed novel SNFO–SMPDM, one case of each class is numerically handled by applying supervised neural networks (SNNs) along with the optimization of Levenberg–Marquardt backpropagation scheme (LMBS), i.e., SNNs–LMBS. A dataset using the traditional variational iteration scheme is designed to compare the proposed results of each case of SNFO–SMPDM. The obtained approximate solutions of each class using the novel SNFO-SMPDM are presented based on the training (80%), authentication (10%) and testing (10%) measures to evaluate the mean square error. Fifteen numbers of neurons, and sigmoid activation function are used in this SNN process. To authenticate the competence, and precision of SNFO–SMPDM, the numerical simulations are accessible by applying the relative measures of regression, error histogram plots, and correlation.

Design of stochastic computational Levenberg Marquardt backpropagation-based technique to investigate temperature distribution of longitudinal moving porous fin

The improvement of thermal exchange is of utmost interest in a wide range of engineering areas. The current study focuses on thermal evaluation involving natural radiation and convection in a fractionally arranged moving longitudinal fin model placed under a magnetic field. We implement the Levenberg Marquardt backpropagation (LMB) algorithm for investigating an innovative use of stochastic numerical computation for analyzing the efficiency of the temperature distribution in a porous moving longitudinal fin. The datasets for LMB have been created using a shooting approach for dynamic systems with varying ranges of different parameters. The validation, testing, and training processes are used to simulate networks using the LMB approach for diverse scenarios of moving porous fin models. The reliability of results is assessed based on the regression measures, absolute error, error histograms, mean square error, and other metrics for fuller numerical modeling of the suggested LMB to investigate the thermal efficiency and effectiveness of porous moving fin.

Predicting hospital admissions for upper respiratory tract complaints: An artificial neural network approach integrating air pollution and meteorological factors.

This study uses artificial neural networks (ANNs) to examine the intricate relationship between air pollutants, meteorological factors, and respiratory disorders. The study investigates the correlation between hospital admissions for respiratory diseases and the levels of PM10 and SO2 pollutants, as well as local meteorological conditions, using data from 2017 to 2019. The objective of this study is to clarify the impact of air pollution on the well-being of the general population, specifically focusing on respiratory ailments. An ANN called a multilayer perceptron (MLP) was used. The network was trained using the Levenberg-Marquardt (LM) backpropagation algorithm. The data revealed a substantial increase in hospital admissions for upper respiratory tract diseases, amounting to a total of 11,746 cases. There were clear seasonal fluctuations, with fall having the highest number of cases of bronchitis (N = 181), sinusitis (N = 83), and upper respiratory infections (N = 194). The study also found demographic differences, with females and people aged 18 to 65years having greater admission rates. The performance of the ANN model, measured using R2 values, demonstrated a high level of predictive accuracy. Specifically, the R2 value was 0.91675 during training, 0.99182 during testing, and 0.95287 for validating the prediction of asthma. The comparative analysis revealed that the ANN-MLP model provided the most optimal result. The results emphasize the effectiveness of ANNs in representing the complex relationships between air quality, climatic conditions, and respiratory health. The results offer crucial insights for formulating focused healthcare policies and treatments to alleviate the detrimental impact of air pollution and meteorological factors.

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.

Modeling of CI engine performance and emission parameters using artificial neural network powered by catalytic co-pyrolytic renewable fuel

Emission and performance parameters of a 4-stroke CI engine operated on a blend of catalytic co-pyrolysis oil with pure diesel, produced through Azadirachta indica seed, waste LDPE (low-density polyethylene), and aluminium oxide (Al2O3) as a catalyst, are modelled in the current work using an Artificial Neural Network (ANN). At 500°C temperature, the highest oil output obtained was 93.91 wt%. The produced liquid fuel possessed similar physical features to that of pure diesel, including density (794 kg/m3) and heating value (44.42 MJ/kg), but lower flash and fire points that would assist in a better and complete combustion of the fuel blend resulting in a better performance and combustion characteristics. Using inputs including brake mean effective pressure, load, brake power, and torque, a developed ANN model was applied to forecast the performance (Brake Thermal Efficiency and Brake Specific Fuel Consumption) along with emission characteristics (Smoke and NOx). The Levenberg-Marquardt back-propagation training technique was applied for emissions and performance characteristics prediction having the best accuracy. Regression coefficients (R2) for predicting BTE, BSFC, NOx, and smoke were all very near to 1: 0.99801, 0.9983, 0.95753, and 0.97467. The study determines that the proposed alternative fuel could be utilized in blend with the pure diesel to in an unmodified diesel engine. It has also been found that artificial neural networks (ANN) could prove to be useful to model and forecast the performance or emissions of renewable fuels in diesel engines, with the potential for these fuels to be employed in transportation.

Classification of coal bursting liability of some chinese coals using machine learning methods

The classification of coal bursting liability (CBL) is essential for the mitigation and management of coal bursts in mining operations. This study establishes an index system for CBL classification, incorporating dynamic fracture duration (DT), elastic strain energy index (WET), bursting energy index (KE), and uniaxial compressive strength (RC). Utilizing a dataset comprising 127 CBL measurement groups, the impacts of various optimization algorithms were assessed, and two prominent machine learning techniques, namely the back propagation neural network (BPNN) and the support vector machine (SVM), were employed to develop twelve distinct models. The models’ efficacy was evaluated based on accuracy, F1-score, Kappa coefficient, and sensitivity analysis. Among these, the Levenberg–Marquardt back propagation neural network (LM-BPNN) model was identified as superior, achieving an accuracy of 96.85%, F1-score of 0.9113, and Kappa coefficient of 0.9417. Further validation in Wudong Coal Mine and Yvwu Coal Industry confirmed the model, achieving 100% accuracy. These findings underscore the LM-BPNN model’s potential as a viable tool for enhancing coal burst prevention strategies in coal mining sectors.

INTELLIGENT NUMERICAL METHOD FOR STUDYING MAXWELL WILLIAMSON NANOFLUID FLOW WITH ACTIVATION ENERGY

The use of artificial intelligence and its techniques has become increasingly widespread in recent times. It is being used to solve stiff non-linear equations. Additionally, nanofluids play a pivotal role in studying heat transfer. All of this was the motivation for doing this work. This work investigates a two-dimensional magnetohydrodynamic stretched flow (2D-MHDSF) of Maxwell Williamson nanofluid (MWNF) affected by bioconvection and activation energy numerically through Levenberg-Marquardt backpropagation method (LMBM)-based artificial neural network approach. The mathematical formulation for the problem was obtained through non-linear partial differential equations (PDEs). The leading PDEs were transmitted into non-linear ordinary differential equations by similarity transformation variables. The reference results for the 2D-MHDSF-MWNF model are produced by the Lobatto IIIA method through different scenarios of specific parameters for the flow velocity, fluid temperature, nanoparticle concentration, and motile density profiles. Using obtained results as a dataset to apply the testing, training, and validation steps of the suggested LMBM for the 2D-MHDSF-MWNF model. The mean squared error, analysis of regression, and error histograms are presented to prove the efficiency and precision of the proposed method. The numerical results of LMBM are displayed as a study of the effects of different physical factors on flow dynamics for 2D-MHDSF-MWNF.

Modelling reverse osmosis process and multiple effect evaporator process of common effluent treatment plant using artificial neural network

This paper presents the study on modeling the performance of Textile and Tannery Common Effluent Treatment Plant (CETP) using Artificial Neural Networks (ANN). The process of Reverse Osmosis (RO) Process and Multiple Effect Evaporator (MEE) process of CETP is modelled using ANNs. Two ANN models were developed to predict the performance of CETP dealing with highly saline effluents. Model-I (RO Model) predicts TDS Rejection (%) by taking pH, Electrical Conductivity (EC), Total Dissolved Solids (TDS), Chemical Oxygen Demand (COD) of RO feed as input parameters thus providing estimate of salt concentration. Model-II (MEE Model) predicts Steam Output needed by taking pH, TDS, Feed flow as input parameters. Levenberg-Marquardt backpropagation (trainlm) algorithm was used as training function for creation of both of ANN models and Hyperbolic Tangent Sigmoid (tansig) was used as transfer function. Separate model validation has been performed to test the predictability of the model and at last prediction accuracy were analysed to show its efficiency in prediction.

Investigating the Impact of Data Normalization Methods on Predicting Electricity Consumption in a Building Using different Artificial Neural Network Models.

The study investigates the impact of data normalization on the prediction of electricity consumption in buildings using four multilayer Artificial Neural Networks (ANN) algorithms: Long Short-Term Memory Networks (LSTM), Levenberg-Marquardt Back-propagation (LMBP), Recurrent Neural Networks (RNN), and General Regression Neural Network (GRNN). Four data normalization approaches, Min-Max Scaling, Mean, Z-score, and Gaussian function were assessed on experimental datasets. The LSTM algorithm, when combined with Min-Max normalization, showed the most favorable predictive capabilities, with a low Coefficient of Variation of the Root Mean Square Error (CVRMSE) of 10.3 and Normalized Mean Bias Error (NMBE) of 0.6. The remaining three normalization approaches showed satisfactory concordance with empirical data, but with slight disparities in precision. The LMBP model, when using Z-score normalization, had favorable performance in forecasting electricity consumption, but the discrepancies across the models were not significant. The Recurrent Neural Network (RNN) model, when used with Gaussian normalization, exhibited the most favorable performance, with the lowest Coefficient of Variation of Root Mean Square Error (CVRMSE) at 11.8 and Normalized Mean Biased Error (NMBE) at 0.6. The Generalized Regression Neural Network (GRNN) model, trained on unprocessed data, exhibited superior performance, with the lowest Coefficient of Variation of Root Mean Square Error (CVRMSE) at 19.2 and NMBE at 1.0. In conclusion, the study highlights the significant influence of data normalization on the predictive capabilities of various ANN models, suggesting that careful use of data normalization techniques can significantly improve the accuracy of electricity consumption forecasting in buildings.

Artificial Neural Network Accuracy Optimization Using Transfer Function Methods on Various Human Gait Walking Environments

A bionic leg with ergonomic functionality can increase the user’s independence. However, an ergonomic bionic leg can be challenged to be developed. One of its challenges is related to functionality, where the bionic leg motor can be rugged to adapt to the user. One of the solutions for the bionic leg challenge is the application of a motor driver controlled by the user’s muscle signal. EMG signal can be utilized as the user’s signal source. The EMG signal is then fed back into the motor device. EMG signals obtained during a natural walking environment can result in smooth and natural movement. This study classifies EMG signals into 8 classes: a controlled walking environment (treadmill walking with various speeds) and a natural walking environment (ground walking, upstairs and downstairs walking). This research aims to optimize the ANN method using transfer function variations. The best method will be used to train EMG-driven motors for future studies related to bionic legs. The best ANN parameter in this research using Levenberg-Marquardt backpropagation as a training algorithm with transfer function pairing of the exponential function: Hyperbolic tangent sigmoid transfer function and SoftMax transfer function with 98.8% accuracy and 0.036 MSE value. The best method from the experiment and ANN classification can be used as a training method for a bionic leg in future research.

Artificial Neural Networks and Experimental Analysis of the Resistance Spot Welding Parameters Effect on the Welded Joint Quality of AISI 304.

The automobile industry relies primarily on spot welding operations, particularly resistance spot welding (RSW). The performance and durability of the resistance spot-welded joints are significantly impacted by the welding quality outputs, such as the shear force, nugget diameter, failure mode, and the hardness of the welded joints. In light of this, the present study sought to determine how the aforementioned welding quality outputs of 0.5 and 1 mm thick austenitic stainless steel AISI 304 were affected by RSW parameters, such as welding current, welding time, pressure, holding time, squeezing time, and pulse welding. In order to guarantee precise evaluation and experimental analysis, it is essential that they are supported by a numerical model using an intelligent model. The primary objective of this research is to develop and enhance an intelligent model employing artificial neural network (ANN) models. This model aims to provide deeper knowledge of how the RSW parameters affect the quality of optimum joint behavior. The proposed neural network (NN) models were executed using different ANN structures with various training and transfer functions based on the feedforward backpropagation approach to find the optimal model. The performance of the ANN models was evaluated in accordance with validation metrics, like the mean squared error (MSE) and correlation coefficient (R2). Assessing the experimental findings revealed the maximum shear force and nugget diameter emerged to be 8.6 kN and 5.4 mm for the case of 1-1 mm, 3.298 kN and 4.1 mm for the case of 0.5-0.5 mm, and 4.031 kN and 4.9 mm for the case of 0.5-1 mm. Based on the results of the Pareto charts generated by the Minitab program, the most important parameter for the 1-1 mm case was the welding current; for the 0.5-0.5 mm case, it was pulse welding; and for the 0.5-1 mm case, it was holding time. When looking at the hardness results, it is clear that the nugget zone is much higher than the heat-affected zone (HZ) and base metal (BM) in all three cases. The ANN models showed that the one-output shear force model gave the best prediction, relating to the highest R and the lowest MSE compared to the one-output nugget diameter model and two-output structure. However, the Levenberg-Marquardt backpropagation (Trainlm) training function with the log sigmoid transfer function recorded the best prediction results of both ANN structures.

A novel approach for modelling and predicting the drying kinetics of couscous grains using artificial neural networks

This paper presents a new approach for modelling and predicting the evolution of moisture content (MC) in couscous grains during drying using artificial neural networks. Couscous grains with an initial moisture content of 42 ± 1% were dried in an oven using the gravimetric method. Experimental data on moisture content versus drying time were obtained for nine groups of measurements at relative humidities of 7, 32 and 75% at drying temperatures of 30, 40 and 50°C. Different parameters of the ANN model, such as three learning algorithms and four activation functions, as well as the number of neurons in the hidden layer, were tested and evaluated using the correlation coefficient (R2) and the mean squared error (MSE) to find the optimal structure without overfitting. The best performing ANN structure consisted of the log sigmoid function in the hidden layer, with 24 neurons and the linear function in the output layer, trained by the Levenberg-Marquardt backpropagation algorithm. A significant agreement of predictions with experimental data was observed, with an R2 value of 0.99999 and an MSE value of 8.2173 ×10−4.

Comprehensive performance analysis of training functions in flow prediction model using artificial neural network

Higher Himalayan catchments are often poorly monitored for hydrological activities involving flood flow prediction for the safety of riverside communities and the successful operation of hydropower projects. This study aimed to estimate the comparative performance of artificial neural network (ANN) based flow prediction models using 10 years of daily river flow data of Kaligandaki catchment at Kotagaun, Nepal, which is a snow-fed catchment in the Himalayan region. The flow prediction models were trained and tested at a hydrological station using the previous 3 days’ river flow data to predict the 1-day ahead flow data. Eight different training functions were employed in an ANN model for comprehensive statistical assessment of accuracy and precision of each training function. The most significant and validated result obtained in this study is the comprehensive comparison of various training functions’ performance, and identification of the most efficient training function for the study case. Among the training functions investigated, the Levenberg-Marquardt backpropagation function exhibits the best performance for the model having Nash-Sutcliffe efficiency, root mean square error and mean absolute error values of 0.866, 209.578 and 75.422, respectively. This study provides a fundamental basis for accurate flow prediction of topographically challenged catchments where hydrological monitoring and data collection may be limited. In particular, this model will help to improve early warning system, hydrological planning, and the safety of riverside communities in the Himalayan region.

Magnetohydrodynamics tangent hyperbolic nanofluid flow across a vertical stretching surface using Levengberg-Marquardt back propagation artificial neural networks

This analysis uses the Levenberg-Marquardt back propagation artificial neural networks (LM-BP-ANNs) approach to demonstrate the mathematical strategy of neural networks for the simulation of MHD Tangent hyperbolic nanofluid (THNF) flow consisting of motile microorganisms through a vertically extending surface. The fluid flow is being investigated in terms of exponential heat source/sink, thermal radiation, and magnetic field. The modeled equations are relegated to the ordinary system of differential equations by substituting similarity variables. The ND-solve approach is applied for the modeled equations to numerically handle and generate a dataset. Several activities, including testing, verification, and training, are performed by creating a scheme for various fluid problems using reference data sets. The precision of LM-BP-ANNs is evaluated using mean square error, curve fitting error histogram, and the regression analysis plot. Furthermore, graphs are used to analyze flow parameters for concentration, momentum, and energy profiles. It has been observed that the velocity field declines as the magnetic field grows stronger. The THNF model for energy, mass, and momentum equations is tested, authenticated, and trained within an average of 10−9. The LM-BP-ANNs accomplish the highest accuracy, with a target date and absolute error reference values in the 10−4 to 10−5 range.

Review on Design and Simulation of Electricity Price Fore Casting Using Artificial Neural Network

Setting the price for electricity is the main task in the reorganized power markets. Forecasting power costs well and precisely has therefore become more crucial. An ANN (Artificial Neural Network) model specifically designed for short-term forecasting of prices in restructuring electricity markets is presented in this research. The input layer, two layers that are concealed, and output layer make up the four layers of the suggested ANN model, which is a perceptron neural network. In place of traditional back propagation, the Levenberg-Marquardt back propagation (LMBP) technique is used for ANN training in order to accelerate convergence. The suggested ANN model is trained using MATLAB, and its effectiveness and performance are shown through a use in the Ontario energy market. Key Word: Fuel cell electric vehicle, high voltage gain IBC, PEMFC, MPPT, RBFN etc.

C@MOF composite material for rapid and efficient capture of gaseous iodine

In addressing the urgent challenge of mitigating gaseous iodine, a highly volatile and hazardous element in nuclear incidents, this study synthesized composite adsorbents with diverse C/Zn molar ratios using MOF and carbon powder. The saturated iodine adsorption at 75 °C exhibited the sequence: CZ-3 (1.15 g g−1) > CZ-2 (1.08 g g−1) > CZ-1 (0.93 g g−1) > C (0.79 g g−1), displaying 2.3–10.1 times increase in adsorption rate compared to carbon powder and Zn-MOF-2. At an elevated temperature of 95 °C, it achieved saturated adsorption of 1.29 g g−1(CZ-3). The adsorbed iodine primarily manifested in the forms of I2, I3-, and I5-. The dynamic maximum iodine adsorption capacity under specific conditions (75 °C, 300 ppm, 100 mL min−1, 0.5 MPa, 4 cm column length, and 6 mm diameter) reached 1077 mg g−1. Leveraging the Levenberg-Marquardt backpropagation neural network (LM-BPNN) algorithm, a superior fit was achieved. This research provides a theoretical foundation for the rapid and efficient treatment of gaseous iodine in nuclear scenarios.

Analysis of chemical reactive nanofluid flow on stretching surface using numerical soft computing approach for thermal enhancement

ABSTRACT In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem’s consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system’s numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified.

Assessing inflation and greenhouse gas emissions interplay via neural network analysis: a comparative study of energy use in the USA, EU, and China

This study examines the relationship between inflation and greenhouse gas (GHG) emissions in three major economies: the United States of America (USA), the European Union (EU), and China. The analysis spans from 1960 to 2021 for the USA and EU, and from 1971 to 2021 for China. A feedforward neural network model, optimized using the Levenberg–Marquardt backpropagation algorithm, was employed to predict GHG emissions based on annual inflation rates and fossil fuel energy consumption. The study integrates historical data on inflation trends with GHG emissions, measured in CO2 equivalents, and fossil fuel energy consumption, expressed as a percentage of total energy use. This multidimensional approach allows for a nuanced understanding of the economic-environmental interplay in these regions. Key findings indicate a nonlinear response of GHG emissions to inflation rates. In the USA, GHG emissions begin to decrease when inflation rates exceed 4.7%. Similarly, in the EU, a steep reduction in emissions is observed beyond a 7.5% inflation rate. China presents a more complex pattern, with two critical inflection points: the first at a 4.5% inflation rate, where GHG emissions start to decline sharply, and the second at a 7% inflation rate, beyond which further increases in inflation do not significantly reduce emissions. A critical global insight is the identification of a uniform inflation rate, around 4.4%, across all regions, at which GHG emissions consistently increase by 1%, hinting at a shared global economic behavior impacting the environment. This discovery is vital for policymakers, emphasizing the need for tailored regional strategies that consider unique economic structures, energy policies, and environmental regulations, alongside a coordinated global approach.