Learning Process Of Neural Network Research Articles

An optimized multilayer perceptron-based network intrusion detection using Gray Wolf Optimization

The exponential growth in the use of network services through the design of various network infrastructures, has led to increased complexities and challenges in the network. A major problem in computer networks is privacy and security breach. Cyber attackers exploit loopholes to infiltrate and disrupt the operation of the network through various attacks. Anomaly-based intrusion detection often employs Artificial Neural Network techniques like Multi-layer Perceptron (MLP) to classify malicious and legitimate traffic. Nevertheless, these techniques are vulnerable to overfitting and require extensive labeled data and computational resources. Consequently, this reduces the accuracy of intrusion detection systems and increases the error detection rate. To minimize the error detection rate of the intrusion detection system, it is necessary to optimize the connection parameters of the MLP neural network such as weights and biases. To this end, we proposed an optimized MLP-based Intrusion Detection using Gray Wolf Optimization (GWOMLP-IDS) to optimize the learning process of the MLP neural network by optimizing weights and biases. GWO aims to select an optimal connection parameter during the learning process to minimize the error rate of intrusion detection. Extensive simulations in Python reveal the effectiveness of the proposed approach in terms of designated performance metrics.

Achieving view-distance and -angle invariance in motion prediction using a simple network

Recently, human motion prediction has gained significant attention and achieved notable success. However, current methods primarily rely on training and testing with ideal datasets, overlooking the impact of variations in the viewing distance and viewing angle, which are commonly encountered in practical scenarios. In this study, we address the issue of model invariance by ensuring robust performance despite variations in view distances and angles. To achieve this, we employed Riemannian geometry methods to constrain the learning process of neural networks, enabling the prediction of invariances using a simple network. Furthermore, this enhances the application of motion prediction in various scenarios. Our framework uses Riemannian geometry to encode motion into a novel motion space to achieve prediction with an invariant viewing distance and angle using a simple network. Specifically, the specified path transport square-root velocity function is proposed to aid in removing the view-angle equivalence class and encode motion sequences into a flattened space. Motion coding by the geometry method linearizes the optimization problem in a non-flattened space and effectively extracts motion information, allowing the proposed method to achieve competitive performance using a simple network. Experimental results on Human 3.6M and CMU MoCap demonstrate that the proposed framework has competitive performance and invariance to the viewing distance and viewing angle.

Individual Buffalo Identification Through Muzzle Dermatoglyphics Images using Deep Learning Approaches

Animal identification is essential for routine farm operations, residue traceback, insurance, and ownership management. Owing to their uniqueness, incorrigible nature, tamperproof over time, environment-friendly, and pain-free, visual biometrics-based animal identification has recently gained momentum over traditional animal identification methods. Among visual biometrics-based cues, muzzle identification is a simple and relatively low-cost method. Therefore, to address the inherent significant limitations of conventional animal identification systems, we undertook this investigation to collect a database of digital images of muzzles that works as a benchmark, to apply deep learning frameworks to identify individual buffaloes from their muzzle images, and to compare their accuracy in terms of their identification capabilities. Muzzle images of 198 Surti buffaloes were subjected to transfer learning and fine-tuning processes in deep-learning neural networks. The performance was recorded for each pre-train model (ResNet50, InceptionV3, VGG16, AlexNet) with different hyperparameters of the epoch, batch size, and learning rate. A perusal of the data revealed that ResNet50 has the highest train accuracy (99.8%) and test accuracy (99.69%) among all four models used. AlexNet has the lowest train accuracy (90.8%) among the models. The findings concluded that all these four models could be applied to identify individual buffaloes; however, ResNet50 had the highest accuracy, and deep learning applications have great potential for individual buffalo identification and are promising tools for precision livestock farming

Prediction of Sand Production from Poorly Consolidated Formations Using Artificial Neural Network: A Case Study, Nahr Umr Formation in Subba Oil Field

Sand production in poorly consolidated formations is a significant challenge to the oil and gas industry, resulting in reduced production and compromised equipment integrity. The oil and gas industry has recently become interested in data analytics because it has significantly simplified, accelerated, and reduced the cost of data visualization. The intriguing new approaches in artificial intelligence development promise to offer long-term solutions to the increasing problems affecting the petroleum industry's operations. Any completion operation in sandstone formations is based on determining whether or not a well will produce sand. It is economically unfavorable to the Nahr Umr Formation to install sand control equipment for wells that don't produce sand. This study aims to create an efficient and precise artificial neural network that can predict sanding in sandstone formations. To achieve this, we developed a two-layered ANN with a back-propagation algorithm using JMP software. The model formulation included various geological and mechanical factors that could impact sand detachment, such as Young’s modulus (YME), Poisson’s ratio, minimum and maximum horizontal stresses (SHMIN and SHMAX), pore pressure, shale volume, and formation strength. The study acquired data from both local fields, specifically the Amarah oilfield, and non-local fields from the literature. Two sets were created from the data: a training set comprising 75% of the data, and a test set comprising 25% of the data, both of which were classified. The speed and accuracy of a learning process in an Artificial Neural Network depends on the size of the data set, the number of hidden layers, and the input parameters. The statistical measures such as accuracy, confusion matrix, root mean square error, and generalized RSquare demonstrate the strong efficacy of the created Artificial Neural Network model. The results indicate a significant likelihood of sand production occurring over the perforation intervals across Su-4 and Su-5 wells. The method's unique feature is its ability to isolate shale areas and identify weak areas capable of producing sand in sandstone formations. In conclusion, it is determined that an Artificial Neural Network employing the back-propagation algorithm is a simple, reliable, and easy-to-use method for accurately predicting sand production.

Research on priority scheduling strategy for smoothing power fluctuations of microgrid tie‐lines based on PER‐DDPG algorithm

AbstractThe variability of renewable energy within microgrids (MGs) necessitates the smoothing of power fluctuations through the effective scheduling of internal power equipment. Otherwise, significant power variations on the tie‐line connecting the MG to the main power grid could occur. This study introduces an innovative scheduling strategy that utilizes a data‐driven approach, employing a deep reinforcement learning algorithm to achieve this smoothing effect. The strategy prioritizes the scheduling of MG's internal power devices, taking into account the stochastic charging patterns of electric vehicles. The scheduling optimization model is initially described as a Markov decision process with the goal of minimizing power fluctuations on the interconnection lines and operational costs of the MG. Subsequently, after preprocessing the historical operational data of the MG, an enhanced scheduling strategy is developed through a neural network learning process. Finally, the results from four scheduling scenarios demonstrate the significant impact of the proposed strategy. Comparisons of reward curves before and after data preprocessing underscore its importance. In contrast to optimization results from deep deterministic policy gradient, soft actor‐critic, and particle swarm optimization algorithms, the superiority of the deep deterministic policy gradient algorithm with the addition of a priority experience replay mechanism is highlighted.

Automatic segmentation of intraluminal thrombosis of abdominal aortic aneurysms from CT angiography using a mixed-scale-driven multiview perception network (M2Net) model

Intraluminal thrombosis (ILT) plays a critical role in the progression of abdominal aortic aneurysms (AAA). Understanding the role of ILT can improve the evaluation and management of AAAs. However, compared with highly developed automatic vessel lumen segmentation methods, ILT segmentation is challenging. Angiographic contrast agents can enhance the vessel lumen but cannot improve boundary delineation of the ILT regions; the lack of intrinsic contrast in the ILT structure significantly limits the accurate segmentation of ILT. Additionally, ILT is not evenly distributed within AAAs; its sparsity and scattered distributions in the imaging data pose challenges to the learning process of neural networks. Thus, we propose a multiview fusion approach, allowing us to obtain high-quality ILT delineation from computed tomography angiography (CTA) data. Our multiview fusion network is named Mixed-scale-driven Multiview Perception Network (M2Net), and it consists of two major steps. Following image preprocessing, the 2D mixed-scale ZoomNet segments ILT from each orthogonal view (i.e., Axial, Sagittal, and Coronal views) to enhance the prior information. Then, the proposed context-aware volume integration network (CVIN) effectively fuses the multiview results.Using contrast-enhanced computed tomography angiography (CTA) data from human subjects with AAAs, we evaluated the proposed M2Net. A quantitative analysis shows that the proposed deep-learning M2Net model achieved superior performance (e.g., DICE scores of 0.88 with a sensitivity of 0.92, respectively) compared with other state-of-the-art deep-learning models. In closing, the proposed M2Net model can provide high-quality delineation of ILT in an automated fashion and has the potential to be translated into the clinical workflow.

Neural Solving Uninterpreted Predicates with Abstract Gradient Descent

Uninterpreted predicate solving is a fundamental problem in formal verification, including loop invariant and Constrained Horn Clauses predicate solving. Existing approaches have been mostly in symbolic ways. While achieving sustainable progress, they still suffer from inefficiency and seem unable to leverage the ever-increasing computility such as GPU. Recently, Neural Relaxation has been proposed to tackle this problem. They treat the uninterpreted predicate-solving task as an optimization problem by relaxing the discrete search process into a learning process of neural networks. However, two bottlenecks keep them from being valid. First, relaxed neural networks cannot match the original semantics rigorously; second, the neural networks are difficult to train to reach global optimization. Therefore, this paper presents a novel discrete neural architecture with the Abstract Gradient Decent (AGD) algorithm to directly solve uninterpreted predicates in the discrete hypothesis space. The abstract gradient is for discrete neurons whose calculation rules are designed in an abstract domain. Our approach conforms to the original semantics, and the proposed AGD algorithm can achieve global optimization satisfactorily. We implement Dasp in the Boxes Abstract Domain to solve uninterpreted predicates in the QF-NIA SMT theory. In the experiments, Dasp has outperformed 7 state-of-the-art tools across three predicate synthesis tasks.

KaTaGCN: Knowledge-Augmented and Time-Aware Graph Convolutional Network for efficient traffic forecasting

Dynamic spatio-temporal dependencies and temporal patterns in traffic series are critical factors affecting traffic forecasting accuracy. Due to the intrinsic challenges of incorporating explicit, logical knowledge into the implicit black-box learning process of neural networks, only a few methods effectively use prior knowledge to improve the learning of traffic forecasting. To tackle this problem, we introduce a new approach called Knowledge-augmented and Time-aware Graph Convolutional Network, namely KaTaGCN. At its core, we have created a knowledge-augmented module that boosts the diffusion weights between closely related adjacent nodes in graph learning. This is achieved by implementing a new loss function. Then, to learn the periodic implicit relationship between these timestamps and traffic signals, the weights and biases are chosen adaptively to be trained based on the timestamps of each sample. Finally, a gated spatio-temporal mapping module regresses high-dimensional embedded features from spatial and temporal dimensions. KaTaGCN is structured without any attention mechanisms or recurrent neural networks. Extensive experimental results on six real-world public traffic datasets demonstrate that KaTaGCN achieves an average improvement of 4.29% in forecasting performance compared with suboptimal results.

Programmable Retention Characteristics in MoS2-Based Atomristors for Neuromorphic and Reservoir Computing Systems.

In this study, we investigate the coexistence of short- and long-term memory effects owing to the programmable retention characteristics of a two-dimensional Au/MoS2/Au atomristor device and determine the impact of these effects on synaptic properties. This device is constructed using bilayer MoS2 in a crossbar structure. The presence of both short- and long-term memory characteristics is proposed by using a filament model within the bilayer transition-metal dichalcogenide. Short- and long-term properties are validated based on programmable multilevel retention tests. Moreover, we confirm various synaptic characteristics of the device, demonstrating its potential use as a synaptic device in a neuromorphic system. Excitatory postsynaptic current, paired-pulse facilitation, spike-rate-dependent plasticity, and spike-number-dependent plasticity synaptic applications are implemented by operating the device at a low-conductance level. Furthermore, long-term potentiation and depression exhibit symmetrical properties at high-conductance levels. Synaptic learning and forgetting characteristics are emulated using programmable retention properties and composite synaptic plasticity. The learning process of artificial neural networks is used to achieve high pattern recognition accuracy, thereby demonstrating the suitability of the use of the device in a neuromorphic system. Finally, the device is used as a physical reservoir with time-dependent inputs to realize reservoir computing by using short-term memory properties. Our study reveals that the proposed device can be applied in artificial intelligence-based computing applications by utilizing its programmable retention properties.

Analysis of The Use of Nguyen Widrow Algorithm in Backpropagation in Kidney Disease

Fast and accurate diagnosis is very important for kidney disease. This research conducts and analyzes by using Nguyen Widrow Algorithm in Back Propagation method in artificial neural network for kidney disease diagnosis with the aim to improve the accuracy in predicting and time efficiency in diagnosing. The Nguyen Widrow algorithm is very capable of accelerating convergence and stabilizing the learning process in artificial neural networks, which is also expected to present a meaningful contribution to the handling of health data. This study uses MATLAB as a platform for algorithm implementation and a dataset of medical records of kidney disease patients collected from a hospital that specializes in treating kidney disease patients. The data pre-processing and artificial neural network modeling stages use the Nguyen Widrow algorithm, while the model training process uses the Back Propagation method. The results showed that the Nguyen Widrow algorithm was able to improve the accuracy of predicting someone suffering from kidney disease compared to using only the Back Propagation method. Analysis of the performance of the model shows a significant improvement in stability and convergence speed during the learning process. This indicates that data processing and medical decision making becomes more efficient. On the other hand, this research also studied the challenges and limitations that will be faced in terms of implementation of the Nguyen Widrow algorithm. Also the sensitivity of the initialization parameters, the need for the quality of the dataset to be used in training the model.This research reveals the ability of the Nguyen Widrow algorithm to improve the performance of artificial neural networks in diagnosing kidney disease. By implementing this algorithm in MATLAB, the results show that the use of the latest data processing technology and analysis tools can provide significant improvements in accuracy and efficiency in the medical field. In addition, this research is expected to provide a new direction in the development of machine learning algorithms for applications in the healthcare field, especially for diagnosing kidney disease. By further utilizing this technology, it contributes significantly to improving the quality of healthcare and treatment outcomes for patients suffering from kidney disease.

RECURSIVE NEURAL NETWORK AS A HIGH-SPEED PLATE COLLISION EMULATOR

Based on a database obtained using a high-speed plate impact model that relates impact parameters and material model parameters to the free surface velocity profile, the study compares the learning process and accuracy of a feedforward artificial neural network and a recursive neural network. A recursive neural network provides a significantly greater accuracy and requires less training time. Using a recursive neural network as a fast model emulator and Bayesian calibration can make it possible to solve the inverse problem of determining the substance model parameters from the free surface velocity profile with a greater accuracy.

Phase transitions in the mini-batch size for sparse and dense two-layer neural networks

The use of mini-batches of data in training artificial neural networks is nowadays very common. Despite its broad usage, theories explaining quantitatively how large or small the optimal mini-batch size should be are missing. This work presents a systematic attempt at understanding the role of the mini-batch size in training two-layer neural networks. Working in the teacher-student scenario, with a sparse teacher, and focusing on tasks of different complexity, we quantify the effects of changing the mini-batch size m. We find that often the generalization performances of the student strongly depend on m and may undergo sharp phase transitions at a critical value mc , such that for m<mc the training process fails, while for m>mc the student learns perfectly or generalizes very well the teacher. Phase transitions are induced by collective phenomena firstly discovered in statistical mechanics and later observed in many fields of science. Observing a phase transition by varying the mini-batch size across different architectures raises several questions about the role of this hyperparameter in the neural network learning process.

A Comparative Study of Javanese Script Classification with GoogleNet, DenseNet, ResNet, VGG16 and VGG19

Purpose: Javanese script is a legacy of heritage or heritage in Indonesia originating from the island of Java needs to be preserved. Therefore, in this study, the classification and identification process of Javanese script letters will be carried out using the CNN method. The purpose of this research is to be able to build a model which can properly classify Javanese script, it can help in the process of recognizing letters in Javanese script easily.Methods: In this study, the Javanese script classification process has been used the transfer learning process of Convolutional Neural Network, namely GoogleNet, DenseNet, ResNet, VGG16 and VGG19. The purpose of using transfer learning is to improve the sequential CNN model, processing can be better and optimal because it utilizes a previously trained model.Result: The results obtained after testing in this study are using the transfer learning method, the GoogleNet model gets an accuracy of 88.75%, the DenseNet model gets an accuracy of 92%, the ResNet model gets an accuracy of 82.75%, the VGG16 model gets an accuracy of 99.25% and the VGG19 model gets an accuracy of 99.50%.Novelty: In previous studies, it is still very rare to discuss the Javanese script classification process using the CNN transfer learning method and which method is the most optimal for performing the Javanese script classification process. In this study, it had been resulted find an effective method to be able to carry out the Javanese script classification process properly and optimally.

Estimator-Based Reinforcement Learning Consensus Control for Multiagent Systems With Discontinuous Constraints.

This article focuses on the optimal consensus control problem for multiagent systems (MASs) with discontinuous constraints. The case of discontinuous constraints is a particular instance of state constraints, which has been studied less but occurs in many practical situations. Due to the discontinuous constraint boundaries, the traditional barrier function-based backstepping methods cannot be used directly. In response to this thorny problem, a novel constraint boundary reconstruction technique is proposed by designing a class of switch-like functions. The technique can convert discontinuous constraint boundaries into continuous ones, and it strictly proves that when the states satisfy the transformed constraint boundaries, the original constraints are also absolutely fulfilled. Meanwhile, with the aid of the barrier function and distributed event-triggered estimator, an improved coordinate transformation is constructed, which can remove the "feasibility condition" and simplify the controller design. In addition, by introducing prediction error and revised term into the learning process of neural networks (NNs), the optimal consensus problem is resolved by constructing a modified reinforcement learning strategy. Finally, the stability of the MASs is testified through the Lyapunov stability theory, and a simulation example verifies the effectiveness of the proposed method.

A New Method for Integrating a Deep Learning Module into Special Object Classification Software

The article discusses a method for integrating a deep learning module into special software based on classical computer vision methods. This software implements the functions of creating panoramic images and their subsequent comparison with the ability to highlight different areas. The integration of deep learning methods is aimed at automating the classification of found objects and solving problems associated with identifying a large number of small objects and noise anomalies. In the process of carrying out the research, an additional neural network generative model was created that improves the quality of classification by increasing the size of the training dataset. This model was implemented in the form of an ensemble of variational autoencoders, which made it possible to simplify the learning process and fine-tuning of neural networks. Also, in order to assess the quality of the ensemble of variational autoencoders, a new method for checking the generated synthetic data was developed. The result of the integration was improved special software capable of classifying the detected found objects of interest with high accuracy.

COMPARISON OF NEURAL NETWORK ARCHITECTURES TO PREDICTING ELECTRICITY CONSUMPTION BY ENTERPRISE

Forecasting of electricity consumption is a key tool for enterprises, energy supply and power grid organizations. Accurate forecasting enables to plan the distribution of limited resources of the power grid facilities, as well as to manage the demand for electricity. In the context of modern demand management technologies, improving the accuracy of forecasting of electricity consumption becomes especially important.&#x0D; &#x0D; The purpose of the study is to improve the accuracy of predicting power consumption by the power supply object using neural networks.&#x0D; &#x0D; Materials and methods. The work used a data set containing a profile of the enterprise’s capacity for a three-month period, as well as additional data, such as time of day, day of the week, weekends and holidays, month. The data set is divided into training and control parts. Preliminary data processing, neural network architecture design, training and testing were carried out. The criteria for the quality of training are the mean absolute error, the mean square error and the coefficient of determination.&#x0D; &#x0D; Research results. In the work, a comparative analysis of three neural network architectures was performed: a one-dimensional convolutional network, a recurrent neural network with long-term and short-term memory, and WaveNet, on the basis of which their indicators of the quality of power consumption forecasting were evaluated. It was shown that all considered architectures of neural networks are suitable for the use in the issue of predicting power consumption. Long-term and short-term memory networks have shown good results in power prediction due to their ability to handle long-term time dependencies. The WaveNet architecture outperformed both long-term and short-term memory model-based recurrent neural networks and one-dimensional convolutional networks by selected criteria.&#x0D; &#x0D; Conclusions. The study led to the conclusion that the use of neural networks, especially architectures with long-term and short-term memory and WaveNet, is an effective approach for predicting power consumption. The quality of forecasting significantly depends on the choice of hyperparameters and preliminary processing of the initial data. Prospect for further research in this area is studying the influence of various factors on the accuracy of forecasting and optimization of the learning process of neural networks.

Simulation of the of the DeepLabv3 neural network learning process for the agricultural fields segmentation

Objective. Monitoring and determining the state of crops in agricultural production requires the use and improvement of neural network methods of artificial intelligence.The aim of the study is to create a mathematical model of the learning process of the DeepLabV3 neural network for intelligent analysis and segmentation of agricultural fields.Method. Based on the newly formed RGB database of images of agricultural fields, marked up into four classes, a neural network of the DeepLabV3 architecture was developed and trained. Approximations of the learning curve by the modified Johnson function are obtained by the methods of least squares and least modules.Result. A statistical assessment of the quality of training and approximation of neural networks to the DeepLabV3 architecture in combination with ResNet 50 was carried out. The constructed DNN family based on DeepLabV3 with ResNet50 showed the efficiency of recognition and sufficient speed in determining the state of crops.Conclusions. Approximation of the neural network learning diagram to the DeepLabV3 architecture, using a modified Johnson function, allows us to estimate the value of the “saturation” of the simulated dependence and predict the maximum value of the neural network metric without taking into account its possible retraining.

Проектирование прикладного программного продукта распознавания и оценки эмоций с использованием нейронной сети

During the analysis of the most common architectures for building neural networks for image analysis – a direct convolutional layer, a recurrent neural network, a convolutional neural network – the authors determined that the last architecture option for the task is the most suitable. The solutions available on the market, although they allow us to recognize emotions, do not evaluate them, and this is an important result for a wide variety of tasks, because such an assessment allows us to more accurately predict the possible future behavior of both individuals and groups of people. The purpose of this article is to design an application software product (application) and develop a prototype that could perform the functions of analyzing emotions and evaluating them. The objectives of this study include the choice of the architecture of the designed application; the development of an algorithm for the operation of the application; the design of the user interface; a description of the neural network learning process and its results, the model of which was defined in the previous article; demonstration of the prototype (control example). The scientific novelty of the projected application lies in the formation of an assessment of the psycho-emotional state of those people whose images of their faces were evaluated. Such an assessment with recommendations can be widely demanded in various branches of human activity, since it is important to be able to express emotions not only to ordinary people, but also to those whose job is to transfer their emotional state to others: business coaches, journalists, actors, animators, dancers, etc. The presence of emotional intelligence is very important at the moment time.

A unified approach of detecting phase transition in time-varying complex networks

Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network’s state and detect a phase transition between different states, to infer the TVCN’s dynamics. A phase of a TVCN is determined by its Forman–Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.

An Enhanced Single-Particle Model Using a Physics-Informed Neural Network Considering Electrolyte Dynamics for Lithium-Ion Batteries

As power sources for electric vehicles, lithium-ion batteries (LIBs) have many advantages, such as high energy density and wide temperature range. In the algorithm design process for LIBs, various battery models with different model structures are needed, among which the electrochemical model is widely used due to its high accuracy. However, the electrochemical model is composed of multiple nonlinear partial differential equations (PDEs) that make the simulating process time-consuming. In this paper, a physics-informed neural network single-particle model (PINN SPM) is proposed to improve the accuracy of the single-particle model (SPM) under high C-rates, while ensuring high solving speed. In PINN SPM, an SPM-Net is designed to solve the distribution of lithium-ion concentration in the electrolyte. In the neural network learning process, a loss function is designed based on the physical constraints brought by the PDEs, which reduces the error of the neural network under dynamic working conditions. Finally, the PINN SPM proposed in this paper can achieve a maximum relative error of up to 1.2% compared with the high-fidelity data generated from the P2D model under various conditions. Additionally, the PINN SPM is 20.8% faster than traditional numerical solution methods with the same computational resources.