Levenberg-Marquardt Optimization Research Articles

Dual-Parameter Prediction of Downhole Supercritical CO2 with Associated Gas Using Levenberg–Marquardt (LM) Neural Network

This research investigates the application of supercritical carbon dioxide (CO2) within carbon capture, utilization, and storage (CCUS) technologies to enhance oil-well production efficiency and facilitate carbon storage, thereby promoting a low-carbon circular economy. We simulate the flow of supercritical CO2 mixed with associated gas (flow rates 3–13 × 104 Nm3/d) in a miniature venturi tube under high temperature and high-pressure conditions (30–50 MPa, 120–150 °C). Accurate fluid property calculations, essential for simulation fidelity, were performed using the R. Span and W. Wagner and GERG-2008 equations. A dual-parameter prediction model was developed based on the simulation data. However, actual measurements only provide fluid types and measurement data, such as pressure, temperature, and venturi differential pressure, to determine the liquid mass fraction (LMF) and total mass flow rate (m), presenting challenges due to complex nonlinear relationships. Traditional formula-fitting methods proved inadequate for these conditions. Consequently, we employed a Levenberg–Marquardt (LM) based neural network algorithm to address this issue. The LM optimizer excels in handling complex nonlinear problems with faster convergence, making it suitable for our small dataset. Through this approach, we formulated dual-parameter model equations to elucidate fluid flow factors, analyzing the impact of multiple parameters on the LMF and the discharge coefficient (C). The resulting model predicted dual parameters with a relative error for LMF of ±1% (Pc = 95.5%) and for m of ±1% (Pc = 95.5%), demonstrating high accuracy. This study highlights the potential of neural networks to predict the behavior of complex fluids with high supercritical CO2 content, offering a novel solution where traditional methods fail.

Mathematical modeling and machine learning-based optimization for enhancing biofiltration efficiency of volatile organic compounds

Biofiltration is a method of pollution management that utilizes a bioreactor containing live material to absorb and destroy pollutants biologically. In this paper, we investigate mathematical models of biofiltration for mixing volatile organic compounds (VOCs) for instance hydrophilic (methanol) and hydrophobic (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}-pinene). The system of nonlinear diffusion equations describes the Michaelis-Menten kinetics of the enzymic chemical reaction. These models represent the chemical oxidation in the gas phase and mass transmission within the air-biofilm junction. Furthermore, for the numerical study of the saturation of 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}-pinene and methanol in the biofilm and gas state, we have developed an efficient supervised machine learning algorithm based on the architecture of Elman neural networks (ENN). Moreover, the Levenberg-Marquardt (LM) optimization paradigm is used to find the parameters/ neurons involved in the ENN architecture. The approximation to a solutions found by the ENN-LM technique for methanol saturation and 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}-pinene under variations in different physical parameters are allegorized with the numerical results computed by state-of-the-art techniques. The graphical and statistical illustration of indications of performance relative to the terms of absolute errors, mean absolute deviations, computational complexity, and mean square error validates that our results perfectly describe the real-life situation and can further be used for problems arising in chemical engineering.

Determination of residual stress field in laser cladding using finite element updating method driven by contour deformation

Laser cladding is a cutting-edge technology widely used in additive manufacturing and surface modification. This process entails rapid melting and solidification driven by laser heating, which induces residual stress within the material. This study presents a data-driven approach to refine the numerical model of laser cladding, simultaneously emphasizing both the temperature characteristics and residual stress distribution within the thermomechanical coupling process. After integrating the residual stress distribution data obtained through the contour method with the molten pool morphology shaped by the thermal effects of laser cladding, a Levenberg-Marquardt optimization algorithm based finite element model updating scheme is proposed to efficiently identify the parameters of double ellipsoid heat source model, which employs parallel computing to reduce the computational time for iterations. The effectiveness of the proposed method is validated using experimental data. Moreover, this approach is adaptable, unaffected by the specimen size and shape, and can accurately predict the residual stress distribution characteristics. Therefore, it offers a robust framework for simulating the mechanisms of residual stress generation in titanium alloy laser cladding.

StarShip: Mitigating I/O Bottlenecks in Serverless Computing for Scientific Workflows

This work highlights the significance of I/O bottlenecks that data-intensive HPC workflows face in serverless environments - an issue that has been largely overlooked by prior works. We propose StarShip, a framework that leverages different storage options and multi-tier functions to reduce I/O overhead by co-optimizing for service time and service cost. StarShip leverages the Levenberg-Marquardt optimization to find an effective solution in a large, complex search space. It outperforms existing methods with a 45% improvement in service time and a 37.6% reduction in service cost.

Experimental and Engineering Simulation of Loss Characteristics of Silicon Steel Wafers Based on Levenberg-Marquardt Optimization Algorithm

Abstract The loss characteristics of 20WTG1500 silicon steel wafers are simulated and studied by using the Epstein square circle method. First, the loss-measured data are fitted based on the classical Bertotti loss model. When working, a Levenberg-Marquardt (L-M) algorithm is proposed to calculate the parameters of the loss model accurately. For the problem of significant calculation errors of hysteresis loss and stray loss in the classical loss separation model, a variable parameter closely related to the magnetic induction intensity is constructed by using the fixed parameter values of the classical loss model. Then, the loss improvement model is proposed. The accuracy of the improved model is proved by comparing the fitting results of the enhanced model with the measured data.

A novel design of layered recurrent neural networks for fractional order Caputo–Fabrizio stiff electric circuit models

Electrical engineering models often rely on complex circuit configurations that facilitate the dynamic flow of electrically charged particles within a closed conductive network. These circuits serve as essential tools for simulating and analyzing diverse electrical systems and components. This paper introduces a study on nonlinear fractional circuits modeling through the development of a stochastic neuro-computational artificial intelligent-based solver to address mathematical models governing the Fractional order Caputo–Fabrizio stiff electric circuit model (FO-CFSECM) by manipulating the knacks of layered recurrent neural networks (LRNNs) trained with Gradient-based local search algorithm (GLA). In fractional calculus, the Caputo–Fabrizio (CF) fractional order derivative (FOD) emerges as a powerful instrument, binding its capabilities to deliver remarkably accurate solutions for fractional stiff systems. The objective of this work is to exploit the numerical treatment comprehensively for the dynamics of fractal Resistor–Capacitor (RC) and fractal Resistor–Inductor (RL) circuit models by introducing the CF fractional operator. Through the application of artificial intelligence-based soft computing and advanced back-propagative deep neural networks, a deeper understanding of the behavior and distinctive characteristics inherent in these models is sought. The Levenberg–Marquardt optimizer serves as an efficient training GLA tool for learning of LRNNs weights of fractal RL/RC circuit models. The comparative studies on variants of FO-CFSECM demonstrate that LRNNs achieve an impressive mean square error (MSE) ranging from 10[Formula: see text] to 10[Formula: see text] and absolute error (AE) within 10[Formula: see text] to 10[Formula: see text]. The accuracy, reliability, and efficiency of LRNNs for solving the FO-CFSECM were further validated through MSE, AE, controlling parameters of state transitions, error histograms, and correlation measures.

Exploring the influence of nanolayer morphology on magnetized tri-hybrid nanofluid flow using artificial neural networks and Levenberg–Marquardt optimization

This study investigates the impact of morphological nanolayers on the thermal conductivity of magnetized tri-hybrid nanofluid flow using artificial neural networks (ANNs) employing the Levenberg–Marquardt (LM-ANN) scheme. Nonlinear partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs) using similarity variables. A dataset covering various parameters such as nanolayer thickness, particle radius, magnetic parameter, expansion/contraction ratio, Schmidt number, volume fraction, and Prandtl number is generated using the Bvp5c numerical algorithm. LM-ANN is then used for testing, training, and validation to analyze approximate solutions for individual cases. Histogram analysis, mean square error (MSE), and regression investigations validate the LM-ANN. The proposed approach closely aligns with suggested and reference findings, showing an accuracy level within 10−10 range. Increasing nanolayer thickness leads to higher effective thermal conductivity. The Nusselt number increases notably with higher hybrid nanoparticle volume fraction. Laminar shape consistently exhibits superior heat transfer performance compared to other shapes. Increasing nanoparticle volume fraction enhances the Nusselt number and reduces skin friction coefficients (SFC). Industry recommendations include integrating nanolayer technologies for improved thermal efficiency.

What if the Covid-19 Pandemic Never Happened Estimation of the Tourist Arrivals for 2020 Via Levenberg-Marquardt Optimization and K-Star (K ) Machine Learning Algorithms

Based on the probability theory, which is used to model uncertainty and randomness in real-world situations, the study aims to understand the impact of uncertain conditions, such as the Covid-19 pandemic, on the accuracy of the algorithms and the resulting losses to a country's tourism industry. The contribution of this paper to the international body of knowledge is twofold: firstly, it advances theoretical understanding of the use of probability theory in modelling real-world problems; and secondly, it offers a methodological approach for estimating tourist arrivals that accounts for the impact of extreme events. To achieve these aims, the Levenberg-Marquardt optimization was first applied to determine the optimal coefficients of the exponential function for estimating tourist arrivals from 1950 to 2020. Next, the K-Star machine learning algorithm was applied to the dataset with and without Covid-19 cases to estimate tourist arrivals.

Comparison of the Artificial Neural Network's Approximations for the Levenberg-Marquardt Algorithm and the Gradient Descent Optimization on Datasets

The approximations obtained by gradient descent optimization on a set of datasets were compared with the results obtained with the Levenberg-Marquardt Optimization Method (LMOM) on the same datasets. The datasets, which comprised three orthogonal databases obtained from MATLAB's Neural Network toolbox accompanying databases, were normalized and serially loaded to the artificial neural network Graphical User Interface (GUI) designed by the researchers. The GUI built with Visual Studio Programming Language (VSPL) implements a gradient descent optimization scheme of the back-propagation algorithm. The characteristics of each database for determination of the termination criteria were approximated from the developed feature extractive iteration algorithm. Revalidation sessions of the LMOM on the sampled datasets showed significant spuriousness in outputted results when compared with the gradient descent optimization results which although slow in attaining convergence produced results that can be closely replicated. Analysis of the F-statistics and the Receiver Operating Characteristics (ROC) for the sampled datasets results of both methods also showed that the gradient descent method demonstrated significant accuracy and parsimony in approximating the nonlinear solutions in the datasets when compared with the results from LMOM processing. Additionally, in this research, an algorithm for deducing and producing the ROC for analyzed Artificial Neural Network (ANN) sessions was also developed and implemented using VSPL.

A parameter determination method of powder burn model based on Levenberg-Marquardt optimization

ABSTRACT The powder burn model is a mathematical model used to characterize the combustion behavior of energetic materials. In this paper, a parameter determination method for the powder burn model is proposed based on the Levenberg-Marquardt (L-M) optimization algorithm, establishing connections between internal ballistics parameters and powder burn model parameters. Taking a 4/1 single-base propellant as an example, the detailed fitting process is presented, and error analysis is conducted. The fittings of the gas state equation and reaction rate equation of powder burn model converge at the 15th and 22nd iterations, respectively. Both fittings displayed a high level of accuracy, with an R-squared value of 0.999. The comparison with the results of the closed bomb experiments demonstrates excellent agreement between pressure-time curves calculated by the powder burn model and the internal ballistics model, confirming their suitability for describing the combustion behavior of propellants. This method provides a foundation for numerically simulating the internal ballistics combustion behavior of energetic materials.

Artificial neural network and multiple linear regression modeling for predicting thermal transmittance of plain-woven cotton fabric

The present research compares a machine learning model with a statistical model, with specific emphasis on artificial neural networks and multiple linear regression models. The aim of this study is to forecast the thermal transmittance of a plain-woven cotton fabric using input data such as thread density measured in ends per inch, picks per inch, and fabric thickness. The artificial neural network is built using a network with feed-forward backpropagation, and the MATLAB software’s training function trainlm is used to modify its weight and basic values based on Levenberg–Marquardt optimization techniques. The sigmoid transfer function is used to set the layer output and measure network performance in terms of the root mean squared error, mean absolute error percentage, and coefficient of determination which were determined. For the artificial neural network prediction model, the root mean squared error and mean absolute error percentage were 1.05 and 3.132%, respectively, while the coefficient of determination was 0.9307. In contrast, the multiple linear regression prediction model had root mean squared error and mean absolute error percentage values of 2.98 and 8.97%, respectively, along with a coefficient of determination of 0.4727. The results reveal that the artificial neural network model outperforms the multiple linear regression model, showing superior accuracy and robustness in capturing the intricate interactions between important fabric parameters (ends per inch, picks per inch, and thickness) and thermal transmittance values. This research emphasizes the efficiency of artificial neural network modeling as a superior tool for forecasting thermal transmittance in textile applications rather than employing the time-consuming trial-and-error process for delivering significant insights for material engineering and energy-efficient design.

StarShip: Mitigating I/O Bottlenecks in Serverless Computing for Scientific Workflows

This work highlights the significance of I/O bottlenecks that data-intensive HPC workflows face in serverless environments - an issue that has been largely overlooked by prior works. To address this challenge, we propose a novel framework, StarShip, which effectively addresses I/O bottlenecks for HPC workflows executing in serverless environments by leveraging different storage options and multi-tier functions, co-optimizing for service time and service cost. StarShip exploits the Levenberg-Marquardt optimization method to find an effective solution in a large, complex search space. StarShip achieves significantly better performance and cost compared to competing techniques, improving service time by 45% and service cost by 37.6% on average over state-of-the-art solutions.

NEURAL NETWORK BASED ESTIMATION OF ECOLOGICAL FOOTPRINT IN TURKEY WITH ECONOMIC AND ENVIRONMENTAL FACTORS

The globe is currently confronted with escalating ecological challenges as a result of the exponential growth of the population, the expansion of industrial activities, the rapid urbanization process, and the heightened levels of consumption. Due to the prevailing ecological issues, there has been an unbridled surge in the demand for natural resources. The emergence of the Ecological Footprint was driven by the observable escalation of environmental degradation, with the primary objective of promoting sustainability. In this study, an Artificial Neural Network (ANN) model was developed for the estimation of ecological footprint. In the first stage, the variables affecting the ecological footprint were determined. It was concluded that there are strong relationships between the independent variables of Gross Domestic Product (GDP), KOF Globalization Index (KOFGI), and Natural Resource Rent (NRR) and the dependent variable of ecological footprint. In the light of this information, the data of GDP (% annual increase), NRR (% GDP) and KOF Globalization Index and ecological footprint data of Turkey between 1970 and 2016 were used to present the ANN model. Feed-Forward Backprop Method, which is one of the multi-layer network models, was applied in the modeling of the ANN. Levenberg-Marquardt optimization, which updates the weight and bias values of the network, was used as the network training function. The study's results suggest that there was a strong correlation between the whole dataset and the model's accuracy, with a close match of 99.316%. Based on the findings, it can be deduced that the developed artificial neural network (ANN) model has a significant level of precision in forecasting the Ecological Footprint.

Dynamic Behavior Forecast of an Experimental Indirect Solar Dryer Using an Artificial Neural Network

This research presents the prediction of temperatures in the chamber of a solar dryer using artificial neural networks (ANN). The dryer is a forced-flow type and indirect. Climatic conditions, temperatures, airflow, and geometric parameters were considered to build the ANN model. The model was a feed-forward network trained using a backpropagation algorithm and Levenberg–Marquardt optimization. The configuration of the optimal neural network to carry out the verification and validation processes was nine neurons in the input layer, one in the output layer, and two hidden layers of thirteen and twelve neurons each (9-13-12-1). The percentage error of the predictive model was below 1%. The predictive model has been successfully tested, achieving a predictor with good capabilities. This consistency is reflected in the relative error between the predicted and experimental temperatures. The error is below 0.25% for the model’s verification and validation. Moreover, this model could be the basis for developing a powerful real-time operation optimization tool and the optimal design for indirect solar dryers to reduce cost and time in food-drying processes.

A novel binocular vision-robot hand-eye calibration method using dual nonlinear optimization and sample screening

To reduce the effects of random errors in vision robotic systems, a double-layer LM (Levenberg- Marquardt) optimization (DLMO) method was designed to improve the calibration accuracy of the robot hand-eye matrix based on the principle of nonlinear optimization. Firstly, a hand-eye matrix equation was established, and the initial value of the hand-eye matrix was solved by using a linear least square method. Secondly, Euler angle transformation was performed on the rotation matrix part in the hand-eye matrix, to ensure the orthogonality of the rotation matrix. Then, an optimization model of the hand-eye matrix was constructed, and the initial value of the hand-eye matrix was optimized for the first time by using the traditional LM nonlinear optimization method. Finally, the optimization model of the hand-eye matrix was modified, and then the LM nonlinear optimization method with the function of sample point screening was used to optimize the hand-eye matrix for the second time. Using the proposed DLMO, the hand-eye calibration tests were carried out on two industrial robots equipped with binocular vision systems. The average position errors of the calibration results were 0.33 mm and 0.51 mm, respectively. The results showed that the accuracy of the proposed calibration method met the working requirements of the vision-robot in the industrial field.

Numerical investigations of ion slip and hall effects on Cattaneo-Christov heat and mass fluxes in darcy-forchheimer flow of Casson fluid within a porous medium, utilizing non-fourier double diffusion theories through artificial neural networks ANNs

The current research focuses on harnessing the computational power of neural networks, notably the Levenberg-Marquardt backpropagation optimization algorithm (ANN-LMBOA), to simulate the behavior of magnetohydrodynamic (MHD) three-dimensional non-Newtonian Darcy-Forchheimer flow of Casson nanofluid over a stretching surface situated within a porous medium. The fluid flow is subject to the influence of Hall and ion slip forces, contributing to its behavior. Additionally, the Cattaneo–Christov heat flux model is incorporated to represent the temperature balance in the boundary layer accurately. Non-Newtonian fluids improve thermal transmission due to their shear-thinning propensity, increased turbulence, and more excellent convective heat transfer. The thermal conductivity of nanofluids is increased by the inclusion of nanoparticles, enabling more effective heat transmission. Buongiorno's model is used for the nanofluid phenomena that concentrate on thermophoresis and Brownian motion. To tackle the flow problem efficiently, the governing equations are transformed into non-linear differential equations using self-similar variables. The ANN-LMBOA algorithm is then employed to solve these equations, providing a practical and accurate approach to the simulation. To train and validate the ANN-LMBOA model, a dataset is generated using the bvp4c numerical method, which can easily handle highly non-linear coupled differential equations. The dataset is created for different scenarios of flow parameters, facilitating comprehensive training, testing, and authentication of the neural network. The accuracy of the ANN-LMBOA model is assessed through various statistical neural network tools, such as MSE, RP, CF graphs, and EH. The study thoroughly investigates flow model parameters related to momentum, energy, and concentration profiles, which are presented using visual representations to understand the system's behavior and characteristics comprehensively. The effects of various parameters of interest like Casson, ion slip, porosity, thermal relaxation, and magnetic parameters on velocity, temperature, and concentration distribution have been studied numerically via ANN-LMBOA networks. The absolute error of reference and target data is obtained in the range of 10−4 − 10−5which proves the best accuracy performance of ANN-LMBOA networks. By raising the Prandtl and Schmidt numbers, solutal, thermal, and diffusional variables, one can reduce the diffusion of mass and heat.

Optimization of effluents using a neural network in the treatment of industrial wastewater

The growth of the planet's population leads to an increase in the problem of access to fresh water. The main sources of water on Earth are brackish and sea water. In connection with the water crisis, water purification becomes an extremely important process, and its achievement is carried out through desalination and various methods of water treatment. In this context, research into the possibility of using neural networks to improve the operation of sewage treatment plants is necessary. The purpose of the research was to optimize and analyze the efficiency of the work of treatment facilities in the treatment of industrial wastewater. Soft computing methods were used to optimize the proposed models. In this study, the exact results of the application of the neural network were determined using analytical and comparative approaches. Treatment of all wastewater and waste generated in the treatment industry involves a number of processes including air flotation, chemical coagulation, settling and biological treatment using fully mixed activated sludge. Various learning functions have been considered, including forward-propagation artificial neural networks (ANNs) such as multilayer perceptron (MLP), cascaded forward-propagation ANNs, and support vector regression (SVR) models. The learning process includes the use of Levenberg-Marquardt optimization algorithms and sequential minimum. The article also provides graphical images illustrating the different types of pollutants, the costs associated with treatment plants, and the color changes in wastewater observed after the treatment process. The obtained results show a high degree of similarity between the predicted and experimental data, which emphasizes the effectiveness of the backpropagation ANN model for accurate predictions. In addition, the integration of machine learning into the production of detergents can be extremely effective in promoting the efficient and sustainable use of water resources. Overall, the paper provides valuable insights into the use of machine learning to address freshwater scarcity

A numerically efficient output-only system-identification framework for stochastically forced self-sustained oscillators

Self-sustained oscillations are ubiquitous in nature and engineering. In this paper, we propose a novel output-only system-identification framework for identifying the system parameters of a self-sustained oscillator affected by Gaussian white noise. A Langevin model that characterizes the self-sustained oscillator is postulated, and the corresponding Fokker–Planck equation is derived from stochastic averaging. From the drift and diffusion terms of the Fokker–Planck equation, unknown parameters of the system are identified. We develop a numerically efficient algorithm for enhancing the accuracy of parameter identification. In particular, a modified Levenberg–Marquardt optimization algorithm tailored to output-only system identification is introduced. The proposed framework is demonstrated on both numerical and experimental oscillators with varying system parameters that develop into self-sustained oscillations. The results show that the computational cost required for performing the system identification is dramatically reduced by using the proposed framework. Also, system parameters that were difficult to be extracted with the existing method could be efficiently computed with the system identification method developed in this study. Pertaining to the robustness and computational efficiency of the presented framework, this study can contribute to an accurate and fast diagnosis of dynamical systems under stochastic forcing.

Machine learning assisted coupled frequency analysis of skewed multi-phase magnetoelectric composite plates with temperature and moisture dependent properties

In this article, the application of an artificial neural network (ANN)-based machine learning (ML) strategy to predict the coupled frequency of geometrically skewed multiphase magnetoelectric (MME) composite plate exposed to hygrothermal environment is presented. The ANN model is trained using a dataset comprising more than one million simulations conducted using an in-house developed finite element formulation. The underlying multiphysics governing equations are derived using Hamilton’s principle and higher-order shear deformation theory (HSDT). The influence of the hygrothermal environment on the elastic stiffness of MME composites is defined by the empirical constants in the constitutive relations. Four prominent combinations of the empirical constants leading to different elastic stiffness relations have been considered in this study. Alongside, the influence of geometrical skewness on the coupled fundamental frequency is also assessed. For the training of the ANN model, the Levenberg–Marquardt optimization algorithm with 30 neurons along with a tangent sigmoid activation function is used. The trained ANN model is tested on an unseen dataset, different from the training data, and it is shown to accurately predict the natural frequency of MME plate with a maximum error of 2.3%. Further, excluding the training time and considering the computational time alone, the ANN model is found to be 6.3 times faster than the FE simulations. It is anticipated that such ML-based reduced order models can be effective in the design process, especially in complex multiphysics problems, such as the one considered in the work, involving a multitude of geometric, loading and material parameters.

Design of Intelligent Neuro-Supervised Networks for Brain Electrical Activity Rhythms of Parkinson's Disease Model.

The objective of this paper is to present a novel design of intelligent neuro-supervised networks (INSNs) in order to study the dynamics of a mathematical model for Parkinson's disease illness (PDI), governed with three differential classes to represent the rhythms of brain electrical activity measurements at different locations in the cerebral cortex. The proposed INSNs are constructed by exploiting the knacks of multilayer structure neural networks back-propagated with the Levenberg-Marquardt (LM) and Bayesian regularization (BR) optimization approaches. The reference data for the grids of input and the target samples of INSNs were formulated with a reliable numerical solver via the Adams method for sundry scenarios of PDI models by way of variation of sensor locations in order to measure the impact of the rhythms of brain electrical activity. The designed INSNs for both backpropagation procedures were implemented on created datasets segmented arbitrarily into training, testing, and validation samples by optimization of mean squared error based fitness function. Comparison of outcomes on the basis of exhaustive simulations of proposed INSNs via both LM and BR methodologies was conducted with reference solutions of PDI models by means of learning curves on MSE, adaptive control parameters of algorithms, absolute error, histogram error plots, and regression index. The outcomes endorse the efficacy of both INSNs solvers for different scenarios in PDI models, but the accuracy of the BR-based method is relatively superior, albeit at the cost of slightly more computations.