This paper presents a new method to improve the convergence speed and efficiency of the Levenberg-Marquardt ALGORITHM. The Levenberg-Marquardt ALGORITHM is a Newton-based method that is efficient in optimization and determining the weights of neural networks compared to other methods, including the backpropagation method. However, the performance of this method depends significantly on the selection of an appropriate damping factor. Among the various methods for determining the damping factor, the Marquardt line search method and methods based on error norm and based on Jacobian norm are mentioned, which in this paper, by examining the strengths and weaknesses of these methods, a combined method is presented to increase the convergence speed. In the proposed method, the search range of the damping factor and, as a result, the value of the adjustment rate parameter is reduced. By making these corrections, the accuracy of the damping factor search is increased and the convergence speed of the proposed method is increased. In order to evaluate the proposed method, learning a neural network to identify several problems including a nonlinear complex function, a regression and a classification task has been simulated and the results show that the proposed method has good efficiency compared to other methods studied and has been able to reduce the learning error to an acceptable level and has a higher convergence speed.

The purpose of this research is to show the use of neural networks in predicting the tides of the Caspian Sea. Forecasting the current level of seawater is very useful in the shipping industry and is one of the most important parameters in marine geodesy, oceanography, and geophysics. Sea level has been done in different ways. Among the factors that affect the instantaneous sea level changes, the tidal factor has been investigated in this research. Nowadays, artificial intelligence methods are used to predict tides, these methods can fill information gaps the above items are among the advantages of intelligent methods in analyzing and predicting tides. Accordingly, this study method has been used in the preparation of this research. The nature of this research is quantitative and applied, and a descriptive research method has been used. In this research, one of the types of artificial intelligence has been worked with, which is neural networks. Neural networks have been used to validate the primary data and predict the Caspian Sea tides in this research. According to the findings obtained by Geo Tide software and neural networks, the water level of the Caspian Sea is decreasing because is clear in this research. It was found that the neural networks are more effective for predicting the tides, the water level of the Caspian Sea will reach -28 meters from the open water level in the future.

The present study compares and predicts the predictive ability of the capital market based on the learning pattern of the Levenberg-Marquardt ALGORITHM, the Gradient descent and the ARIMA ALGORITHM. For this purpose, market data were used in the period from 1394 to 1397, and more than 75% of these data were used as TRAINING data prior to 1397, and one year end data were used as data. The results of the evaluation of the research data show that artificial neural networks have a high capacity for price prediction. The results also showed that in both TRAINING data series from 1394 to 1396 and experimental of 1397 the comparison of the results and performance of ARIMA neural networks (ARIMA) showed that the neural network had higher predictive power in Comparing with the performance and prediction accuracy of two types of neural networks with the Levenberg-Marquardt learning ALGORITHM and the Gradient descent learning ALGORITHM using the Levenberg-Marquardt learning ALGORITHM has been able to increase the neural network prediction accuracy And reduce its error, so, the results of the present study show, the Levenberg-Marquardt learning ALGORITHM improves the predictive power of the neural network.

A neural network (ANN) model employing the Levenberg-Marquardt ((LM)) ALGORITHM was formulated and employed to study the functionality of both conventional (CSS) and modified (MSSW and MSSU) solar distillation systems. Numerous input factors, comprising solar irradiance, wind speed, atmospheric conditions, glass properties, and water temperatures, were carefully selected, with the yield of distilled water serving as the target variable. The model underwent a process of testing, TRAINING, and validation utilizing empirical data obtained from CSS, MSSW, and MSSU setups, achieving a confidence level of 95%. After validation, the model's capabilities were utilized to forecast the distilled water output based on a distinct set of input parameters. The outcomes unveiled a negligible deviation, with a maximum disparity of 3.1% and 4.6% observed in comparison to the experimental findings for MSSW, and MSSU setups, respectively, thereby signifying a substantial agreement between theoretical predictions and experimental observations. Furthermore, the model exhibited outstanding accuracy in contrast to well-established numerical models proposed by several researchers, thereby demonstrating its efficacy in predicting the performance of solar stills.

In this paper, we present a new approach for solving absolute value equation (AVE) which use Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradient methods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descent direction by the Levenberg-Marquardt direction. The descent property of the direction generated by new ALGORITHM in each iteration is established. Also, the global convergence of such a method are established under some mild assumptions. Some numerical results are reported. In this paper, we present a new approach for solving absolute value equation (AVE) which use Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradient methods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descent direction by the Levenberg-Marquardt direction. The descent property of the direction generated by new ALGORITHM in each iteration is established. Also, the global convergence of such a method are established under some mild assumptions. Some numerical results are reported.

In this paper, the diffusion coefficient in a normal tissue and tumor are to be estimated by the method of inverse problems. At the beginning, distribution of drug (with the assumption of uniform and isentropic diffusion coefficient) in the tissue is considered as the direct problem. In the direct problem, the governing equation is the convection–diffusion, which is the generalized form of Fick’s law. Here, a source and a sink are defined; the source as the rate of solute transport per unit volume from blood vessels into the interstitial space and the sink as the rate of solute transport per unit volume from the interstitial space into lymph vessels are added to this equation. To solve the direct problem, the finite difference method has been considered. Additionally, the diffusion coefficient of a normal tissue and tumor will be approximated by parameter estimation method of Levenberg-Marquardt. This method is based on minimizing the sum of squared errors which, in the present study considered error is the difference of the estimated concentration and the concentration measured by medical images (simulated numerically). Finally, the results obtained by Levenberg-Marquardt method have provided an acceptable estimation of diffusion coefficient in normal tissue and tumor.

The unique properties of carbon monoxide and its high combustibility have led to the creation of various ‎sensors, such as electrochemical sensors and different circuits, to read its output. In this article, a deflection-type ‎Wheatstone bridge is used to measure changes in the sensor resistance, and the output voltage is connected to a 12-‎bit analog-to-digital converter through an adjustable precision amplifier. Next, a new method is proposed for self-calibrating the CO sensor. The Levenberg-Marquardt backpropagation ALGORITHM ((LM)BP) is utilized in the Artificial ‎Neural Network model to minimize the Mean Squared Error (MSE) and identify the most suitable parameters in the ‎proposed method.‎‏ ‏The model under consideration has been developed and trained using real-time data.‎‏ ‏Based on ‎the experimental and evaluation outcomes, it can be concluded that the suggested model has an MSE value of ‎‎0.28249 and an R2 coefficient of determination of 0.99992, indicating high accuracy and precision. The proposed ‎sensor and calibration method have potential applications in various applications, including industrial and domestic ‎environments where CO monitoring is necessary.‎

In this paper, an Artificial Neural Network (ANN) is designed for the determination of unconfined aquifer parameters: transmissibility, storage coefficient, specific yield, and delay index. The network is trained for the well function of unconfined aquifers by the back propagation technique and adopting the Levenberg-Marquardt ((LM)) optimization ALGORITHM. By applying the principal component analysis (PCA) on the TRAINING data sets the topology of the network is reduced and fixed to [3×6×3] regardless of number of records in the pumping test data. The network generates the optimal match point coordinates for any individual real pumping test data set. The match point coordinates are then incorporated with Boulton analytical solution (1963) and the aquifer parameter values are determined. The generalization ability and performance of the developed network is evaluated with 100/000 sets of synthetic data and its accuracy is compared with that of the type curve matching technique by two sets of real field data. The proposed network is recommended as a simpler and more reliable alternative for the determination of unconfined aquifer parameters compare to the conventional type-curve matching techniques.