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In the present arena, the tools of artificial intelligence (AI) play a significant role in research across various fields by enabling advanced data analysis, pattern recognition and decision-making. This research work presents the numerical investigation of bioconvective micropolar nanofluidic model (BCMNFM) by employing the knacks of AI-based nonlinear autoregressive (NAR) approach with a combination of backpropagated Levenberg–Marquardt neural networks (BLMNNs) represented as NAR-BLMNNs. This research work investigates the flow design to highlight the attributes of mass and heat exchange. A dataset for BCMNFM is created by applying the Adam numerical procedure by variation of unsteadiness parameter ($A)$, magnetic field parameter ($M),$ thermophoresis parameter (Nt), Brownian motion parameter (Nb), bioconvection Peclet number (Pe) and spin gradient viscosity parameter ($\lambda ).$ The skills of AI-based NAR-BLMNNs technique is then utilized on the dataset created for BCMNFM to investigate the approximate solutions. The achieved and impactful values of performance consistently range between $E^{-10}$ and $E^{-14}$ across all scenarios of BCMNFM. The precision and the validation of predicted approach NAR-BLMNNs is exceptionally established by the graphical demonstration for all scenarios of MSE, regression metrics, error histograms and time series graphs. The numerical calculations attained through AI-based NAR-BLMNNs technique further rationalize the precision of the proposed methodology for solving the BCMNFM effectively and efficiently.

In this paper, calculations of the $(n,t)$ reaction cross-sections at 14.5 MeV have been presented by utilizing artificial neural network algorithms (ANNs). The systematics are based on the account for the non-equilibrium reaction mechanism and the corresponding analytical formulas of the pre-equilibrium exciton model. Experimental results, obtained from the EXFOR database, have been used to train the ANN with the Levenberg–Marquardt (LM) algorithm which is a feed-forward algorithm and is considered one of the well-known and most effective methods in neural networks. The Regression $(R)$ values for the ANN estimation have been determined as 0.9998, 0.9927 and 0.9895 for training, testing and for all process. The $(n,t)$ reaction cross-sections have been reproduced with the TALYS 1.95 and the EMPIRE 3.2 codes. In summary, it has been demonstrated that the ANN algorithms can be used to calculate the $(n,t)$ reaction cross-section with the semi-empirical systematics.

The study of the behavior of bioconvective nanofluid model (BC-NFM) was explored using bioconvection properties in the computational analysis of magnetized nanofluid flow that was convectively heated, which is critical for applications in energy systems and biomedical devices. We implemented a backpropagated Levenberg–Marquardt neural network approach (BLMNNA) to enhance the analysis and prediction accuracy of such fluid flows. Using the Adams numerical technique, we generated a comprehensive dataset for eight distinct scenarios by variation of thermophoresis parameter, Rayleigh number, Deborah parameter, Hartman number, Prandtl number, bioconvection Lewis number, and Schmidt number to train and test our model. The results demonstrate significant improvements in prediction accuracy and computational efficiency compared to traditional numerical solvers. The steps of training, testing, and validating the developed BLMNNA are used to get the desired numerical solutions of BC-NFM for various instances. The worth and accuracy of the stochastic numerical solutions of BC-NFM are established and authenticated by the outputs of the designed methodology BLMNNA through Adaptation graphs of Mean Square Error, regression studies, plots of error histogram and index of state transition. Excellent measurements of performance in terms of MEAN SQUARE ERROR are achieved at level 9.76E${}^{-10}$, 1.41E${}^{-09}$, 1.79E${}^{-10}$, 1.22E${}^{-9}$, 8.49E${}^{-09}$, 7.19E${}^{-08}$, 9.72E${}^{-09}$, and 9.35E${}^{-10}$ against 69, 73, 96, 76, 237, 86, 120, and 33 epochs. The significant connection between the proposed and reference findings demonstrates the validity of the BLMNNA based on error analysis, which ranges from E${}^{-02}$ to E${}^{-08}$ for all situations. The results show that the proposed neural network approach achieves a high level of accuracy, closely matching the outcomes obtained from the numerical solver. The method provides an efficient and precise solution for the analysis of complex fluid flow problems, representing a significant advancement over traditional numerical techniques.

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.

In this study, an intelligent computing framework is presented to explore the influence of unpredictable environmental factors on the spread of infections. A stochastic non-linear SIS epidemic model (SISEM) is examined that incorporates a non-linear incidence rate, and impact of random fluctuations on the disease transmission. The knacks of artificial neural networks Levenberg–Marquardt (ANNLMA) technique are exploited to illustrate the behavioral complexities of stochastic non-linear SISEM, which explores the dynamics of disease transmission in a stochastic environment and provides insights into the interactions between susceptible and infectious populations. The Milstein approach of order 1 generates a dataset for the proposed ANNLMA technique by varying integrated parameters, such as the rates of recovery, death, disease transmission, noise standard deviation and the entire population, for various SISEM scenarios. The referenced dataset is randomly divided into test, validation and train sets for the weight learning of the proposed ANNLMA. The viability of the ANNLMA is measured using intensive simulation-based investigations through analysis of mean squared errors, histograms, regression and autocorrelation studies. The investigations highlighted that the ANNLMA results closely match the reference results, illustrating convergence within the 10${-2}^{}$ to 10${}^{-7}$ range, indicating the validity of the proposed methodology.

This research work presents the numerical solution of the Darcy–Forchheimer flow of Casson nanofluidic model (DFFCNFM) on stretching sheets with Newtonian heating by utilizing a combination of nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt computational approach. The presented study investigates the impact of electroosmosis forces on the boundary layer of the Casson nanofluid, focusing on viscous and Joule dissipations. A dataset for DFFCNFM is generated for the different events with backward differentiation formula (BDF) by varying Casson fluid parameter ($\beta )$, permeability parameter (Da), electric parameter ($E_1)$, Reynolds number (Re) relative to stretching velocity, magnetic field ($M)$, Eckert number (Ec), and Prandtl number (Pr). The artificial intelligence-inspired technique via nonlinear input–output neural networks with backpropagation of Levenberg–Marquardt is utilized from the generated dataset for DFFCNFM to find the approximate solutions. The satisfactory performance levels, as indicated by the mean square error (MSE), have been attained consistently with magnitude around 10${}^{-12}$–10${}^{-14}$ for all scenarios of DFFCNFM. The precision and performance validation is effectively established by the negligible MSE, close proximity to the unit value of regression metric, and the distribution of instances in error-histograms.

Residual stress in the machined surface and subsurface is affected by materials, machining conditions, and tool geometry and can affect the component life and service quality significantly. Empirical or numerical experiments are commonly used for determining residual stresses but these are very expensive. There has been an increase in the utilization of minimum quantity lubrication (MQL) in recent years in order to reduce the cost and tool/part handling efforts, while its effect on machined part residual stress, although important, has not been explored. This paper presents a hybrid neural network that is trained using Simulated Annealing (SA) and Levenberg-Marquardt Algorithm (LM) in order to predict the values of residual stresses in cutting and radial direction on the surface and within the work piece after the MQL face turning process. Once the ANN has successfully been trained, an optimization procedure, using Genetic Algorithm (GA), is applied in order to find the best cutting conditions in order to minimize the surface tensile residual stresses and maximize the compressive residual stresses within the work piece. The optimization results show that the usage of MQL decreases the surface tensile residual stresses and increases the compressive residual stresses within the work piece.