Artificial Neural Networks to Solve the Singular Model with Neumann–Robin, Dirichlet and Neumann Boundary Conditions

Nisar, Kashif; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Ibrahim, Ag Asri Ag; Rodrigues, Joel J. P. C.; Mahmoud, S.R.; Chowdhry, Bhawani Shankar; Gupta, Manoj

doi:10.3390/s21196498

Cited by 9 publications

(6 citation statements)

References 50 publications

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“…For many years, neural networks [5][6][7][8] have been investigated, and they have recently made significant advances in the field of computer vision [9]. Deep neural network (DNN) models outperform standard machine learning models, especially when it comes to analyzing big annotated datasets [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Models for Breast Cancer Detection via Transfer Learning Technique

Singh¹,

Rawat²,

Gupta³

et al. 2023

CMC

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Currently, breast cancer has been a major cause of deaths in women worldwide and the World Health Organization (WHO) has confirmed this. The severity of this disease can be minimized to the large extend, if it is diagnosed properly at an early stage of the disease. Therefore, the proper treatment of a patient having cancer can be processed in better way, if it can be diagnosed properly as early as possible using the better algorithms. Moreover, it has been currently observed that the deep neural networks have delivered remarkable performance for detecting cancer in histopathological images of breast tissues. To address the above said issues, this paper presents a hybrid model using the transfer learning to study the histopathological images, which help in detection and rectification of the disease at a low cost. Extensive dataset experiments were carried out to validate the suggested hybrid model in this paper. The experimental results show that the proposed model outperformed the baseline methods, with F-scores of 0.81 for DenseNet + Logistic Regression hybrid model, (F-score: 0.73) for Visual Geometry Group (VGG) + Logistic Regression hybrid model, (F-score: 0.74) for VGG + Random Forest, (F-score: 0.79) for DenseNet + Random Forest, and (F-score: 0.79) for VGG + Densenet + Logistic Regression hybrid model on the dataset of histopathological images.

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Section: Introductionmentioning

confidence: 99%

Hybrid Models for Breast Cancer Detection via Transfer Learning Technique

Singh¹,

Rawat²,

Gupta³

et al. 2023

CMC

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“…Fig. 5 shows the architecture of channel attention and spatial attention, which are situated between ResNet layers [48][49][50][51]. We have experimented with an attention mechanism with a baseline, CNN, and Resnet50 on the chosen dataset and observed the improvement in the performance parameters and we have compared the same with a pre-trained model on the same dataset.…”

Section: Resnet-50 With Attentionmentioning

confidence: 99%

Deep Attention Network for Pneumonia Detection Using Chest X-Ray Images

Singh¹,

Rawat²,

Gupta³

et al. 2023

Computers, Materials &Amp; Continua

Self Cite

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In computer vision, object recognition and image categorization have proven to be difficult challenges. They have, nevertheless, generated responses to a wide range of difficult issues from a variety of fields. Convolution Neural Networks (CNNs) have recently been identified as the most widely proposed deep learning (DL) algorithms in the literature. CNNs have unquestionably delivered cutting-edge achievements, particularly in the areas of image classification, speech recognition, and video processing. However, it has been noticed that the CNN-training assignment demands a large amount of data, which is in low supply, especially in the medical industry, and as a result, the training process takes longer. In this paper, we describe an attentionaware CNN architecture for classifying chest X-ray images to diagnose Pneumonia in order to address the aforementioned difficulties. Attention Modules provide attention-aware properties to the Attention Network. The attentionaware features of various modules alter as the layers become deeper. Using a bottom-up top-down feedforward structure, the feedforward and feedback attention processes are integrated into a single feedforward process inside each attention module. In the present work, a deep neural network (DNN) is combined with an attention mechanism to test the prediction of Pneumonia disease using chest X-ray pictures. To produce attention-aware features, the suggested network was built by merging channel and spatial attention modules in DNN architecture. With this network, we worked on a publicly available Kaggle chest X-ray dataset. Extensive testing was carried out to validate the suggested model. In the experimental results, we attained an accuracy of 95.47% and an F-score of 0.92, indicating that the suggested model outperformed against the baseline models.

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“…The boundary conditions are the Dirichlet boundary condition (i.e., the value of the function on a given boundary) and the Neumann boundary condition (i.e., the value of the normal guide on a given boundary). It was shown in [10] that in bounded domains with Dirichlet or Neumann boundary conditions, we can use more complex versions of the equations based on Brownian motion to reduce the errors in the equations. Some common methods for solving high-dimensional elliptic equations are, for example, the Calder´ on-Zygmund type estimate [6], and the separation of variables method [7] for specific cases in high-dimensional elliptic equations, where the hypothetical solution can be expressed by decomposing the multidimensional problem into the form of a product of a series of one-dimensional problems, thus transforming the high-dimensional elliptic equations into a series of one-dimensional ordinary differential equations.…”

Section: Elliptic Equation and Feynman-kac Formulamentioning

confidence: 99%

A Method for Solving Global Solutions to Partial Differential Equations Based on the Annealing Algorithm and Polynomial Regression for the Feynman-Kac Formulation

2023

AJMS

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At present, the global solution of PDE is usually obtained by the Feynman-Kac formula and then constructed by the interpolation method. In this paper, a polynomial fitting method based on the annealing algorithm is proposed to replace the interpolation method to construct the global solution. The simulated annealing algorithm is used to determine the coefficients of the fitting polynomials to obtain higher accuracy. The numerical results show that the improved model has less error than the model obtained by the interpolation method, and the annealing algorithm has a great contribution to improving the accuracy. Then the convergence analysis of the time step, simulation number, and polynomial order is carried out, and the result shows that the convergence is good. Finally, because the Feynman-Kac formula is used to determine the numerical solution, the method is expected to be applied to high-dimensional problems.

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Artificial Neural Networks to Solve the Singular Model with Neumann–Robin, Dirichlet and Neumann Boundary Conditions

Cited by 9 publications

References 50 publications

Hybrid Models for Breast Cancer Detection via Transfer Learning Technique

Hybrid Models for Breast Cancer Detection via Transfer Learning Technique

Deep Attention Network for Pneumonia Detection Using Chest X-Ray Images

A Method for Solving Global Solutions to Partial Differential Equations Based on the Annealing Algorithm and Polynomial Regression for the Feynman-Kac Formulation

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