scholarly journals Solving Differential Equations Using Feedforward Neural Networks

2021 ◽  
pp. 385-399
Author(s):  
Wilson Guasti Junior ◽  
Isaac P. Santos
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Differential Equations ◽  
Feedforward Neural Networks ◽  
Activation Functions ◽  
Learning Models ◽  
Python Language ◽  
The Neural Network ◽  
Minimization Methods

Abstract In this work we explore the use of deep learning models based on deep feedforward neural networks to solve ordinary and partial differential equations. The illustration of this methodology is given by solving a variety of initial and boundary value problems. The numerical results, obtained based on different feedforward neural networks structures, activation functions and minimization methods, were compared to each other and to the exact solutions. The neural network was implemented using the Python language, with the Tensorflow library.

scholarly journals Exploring deep neural networks via layer-peeled model: Minority collapse in imbalanced training

2021 ◽  
Vol 118 (43) ◽  
pp. e2103091118
Author(s):  
Cong Fang ◽  
Hangfeng He ◽  
Qi Long ◽  
Weijie J. Su
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Deep Neural Networks ◽  
Model Minority ◽  
Tight Frame ◽  
Learning Models ◽  
The Neural Network ◽  
Long Time ◽  
Topmost Layer

In this paper, we introduce the Layer-Peeled Model, a nonconvex, yet analytically tractable, optimization program, in a quest to better understand deep neural networks that are trained for a sufficiently long time. As the name suggests, this model is derived by isolating the topmost layer from the remainder of the neural network, followed by imposing certain constraints separately on the two parts of the network. We demonstrate that the Layer-Peeled Model, albeit simple, inherits many characteristics of well-trained neural networks, thereby offering an effective tool for explaining and predicting common empirical patterns of deep-learning training. First, when working on class-balanced datasets, we prove that any solution to this model forms a simplex equiangular tight frame, which, in part, explains the recently discovered phenomenon of neural collapse [V. Papyan, X. Y. Han, D. L. Donoho, Proc. Natl. Acad. Sci. U.S.A. 117, 24652–24663 (2020)]. More importantly, when moving to the imbalanced case, our analysis of the Layer-Peeled Model reveals a hitherto-unknown phenomenon that we term Minority Collapse, which fundamentally limits the performance of deep-learning models on the minority classes. In addition, we use the Layer-Peeled Model to gain insights into how to mitigate Minority Collapse. Interestingly, this phenomenon is first predicted by the Layer-Peeled Model before being confirmed by our computational experiments.

scholarly journals Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Idris Kharroubi ◽  
Thomas Lim ◽  
Xavier Warin
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Learning Approach ◽  
The Neural Network ◽  
Machine Learning Approach ◽  
Mesh Grid

AbstractWe study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

scholarly journals Rain–Induced Flood Prediction for Niger Delta Sub-Region of Nigeria Using Neural Networks

2020 ◽  
Vol 5 (9) ◽  
pp. 1124-1130
Author(s):  
Ledisi Giok Kabari ◽  
Young Claudius Mazi
Keyword(s):  
Neural Network ◽  
Climate Change ◽  
Neural Networks ◽  
Niger Delta ◽  
Feedforward Neural Networks ◽  
Flood Prediction ◽  
The Neural Network ◽  
Significant Damage ◽  
Weather Underground ◽  
Short Term Prediction

Climate change generates so many direct and indirect effects on the environment.  Some of those effects have serious consequences. Rain-induced flooding is one of the direct effects of climate change and its impact on the environment is usually devastating and worrisome. Floods are one of the most commonly occurring disasters and have caused significant damage to life, including agriculture and economy. They are usually caused in areas where there is excessive downpour and poor drainage systems. The study uses Feedforward Multilayer Neural Network to perform short-term prediction of the amount of rainfall flood for the Niger Delta   sub region of Nigeria given previous rainfall data for a specified period of time. The data for training and testing of the Neural Network was sourced from Weather Underground official web site https://www.wunderground.com.  An iterative Methodology was used and implemented in MATLAB. We adopted multi-layer Feedforward Neural Networks. The study accurately predicts the rain-induced flood for the Niger Delta   sub region of Nigeria.

Comprehensive Overview of Neural Networks and Its Applications in Autonomous Vehicles

2019 ◽  
pp. 159-173
Author(s):  
Jay Rodge ◽  
Swati Jaiswal
Keyword(s):  
Neural Network ◽  
Artificial Intelligence ◽  
Neural Networks ◽  
Deep Learning ◽  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Learning Algorithms ◽  
Activation Functions ◽  
Comprehensive Overview ◽  
Unit Component

Deep learning and Artificial intelligence (AI) have been trending these days due to the capability and state-of-the-art results that they provide. They have replaced some highly skilled professionals with neural network-powered AI, also known as deep learning algorithms. Deep learning majorly works on neural networks. This chapter discusses about the working of a neuron, which is a unit component of neural network. There are numerous techniques that can be incorporated while designing a neural network, such as activation functions, training, etc. to improve its features, which will be explained in detail. It has some challenges such as overfitting, which are difficult to neglect but can be overcome using proper techniques and steps that have been discussed. The chapter will help the academician, researchers, and practitioners to further investigate the associated area of deep learning and its applications in the autonomous vehicle industry.

Sign Board Recognition Based on Convolutional Neural Network Using Yolo-3

2020 ◽  
Vol 17 (8) ◽  
pp. 3478-3483
Author(s):  
V. Sravan Chowdary ◽  
G. Penchala Sai Teja ◽  
D. Mounesh ◽  
G. Manideep ◽  
C. T. Manimegalai
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Object Detection ◽  
Convolutional Neural Network ◽  
Road Accidents ◽  
Learning Models ◽  
The Neural Network

Road injuries are a big drawback in society for a few time currently. Ignoring sign boards while moving on roads has significantly become a major cause for road accidents. Thus we came up with an approach to face this issue by detecting the sign board and recognition of sign board. At this moment there are several deep learning models for object detection using totally different algorithms like RCNN, faster RCNN, SPP-net, etc. We prefer to use Yolo-3, which improves the speed and precision of object detection. This algorithm will increase the accuracy by utilizing residual units, skip connections and up-sampling. This algorithm uses a framework named Dark-net. This framework is intended specifically to create the neural network for training the Yolo algorithm. To thoroughly detect the sign board, we used this algorithm.

scholarly journals Increasing of Thermal Images Resolution Using Deep Learning Neural Networks

2021 ◽  
Vol 25 (3) ◽  
pp. 31-35
Author(s):  
Piotr Więcek ◽  
Dominik Sankowski
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Execution Time ◽  
High Accuracy ◽  
New Method ◽  
Residual Network ◽  
Thermal Images ◽  
The Neural Network

The article presents a new algorithm for increasing the resolution of thermal images. For this purpose, the residual network was integrated with the Kernel-Sharing Atrous Convolution (KSAC) image sub-sampling module. A significant reduction in the algorithm’s complexity and shortening the execution time while maintaining high accuracy were achieved. The neural network has been implemented in the PyTorch environment. The results of the proposed new method of increasing the resolution of thermal images with sizes 32 × 24, 160 × 120 and 640 × 480 for scales up to 6 are presented.

scholarly journals Convolutional neural network for image classification based on transfer learning technique

2021 ◽  
Author(s):  
Ghassan Mohammed Halawani
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Convolutional Neural Network ◽  
Image Classification ◽  
Transfer Learning ◽  
Learning Networks ◽  
The Neural Network ◽  
Learning Technique ◽  
Common Architecture

The main purpose of this project is to modify a convolutional neural network for image classification, based on a deep-learning framework. A transfer learning technique is used by the MATLAB interface to Alex-Net to train and modify the parameters in the last two fully connected layers of Alex-Net with a new dataset to perform classifications of thousands of images. First, the general common architecture of most neural networks and their benefits are presented. The mathematical models and the role of each part in the neural network are explained in detail. Second, different neural networks are studied in terms of architecture, application, and the working method to highlight the strengths and weaknesses of each of neural network. The final part conducts a detailed study on one of the most powerful deep-learning networks in image classification – i.e. the convolutional neural network – and how it can be modified to suit different classification tasks by using transfer learning technique in MATLAB.

scholarly journals Envision Foundational of Convolution Neural Network

2021 ◽  
Vol 10 (6) ◽  
pp. 54-60
Author(s):  
M Venkata Krishna Reddy* ◽  
Pradeep S.
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Computer Graphics ◽  
Convolutional Neural Networks ◽  
Generative Models ◽  
Activation Functions ◽  
Machine Learning Classification ◽  
Network Intrusion ◽  
Recent Advances

1. Bilal, A. Jourabloo, M. Ye, X. Liu, and L. Ren. Do Convolutional Neural Networks Learn Class Hierarchy? IEEE Transactions on Visualization and Computer Graphics, 24(1):152–162, Jan. 2018. 2. M. Carney, B. Webster, I. Alvarado, K. Phillips, N. Howell, J. Griffith, J. Jongejan, A. Pitaru, and A. Chen. Teachable Machine: Approachable Web-Based Tool for Exploring Machine Learning Classification. In Extended Abstracts of the 2020 CHI Conference on Human Factors in Computing Systems, CHI ’20. ACM, Honolulu, HI, USA, 2020. 3. A. Karpathy. CS231n Convolutional Neural Networks for Visual Recognition, 2016 4. M. Kahng, N. Thorat, D. H. Chau, F. B. Viegas, and M. Wattenberg. GANLab: Understanding Complex Deep Generative Models using Interactive Visual Experimentation. IEEE Transactions on Visualization and Computer Graphics, 25(1):310–320, Jan. 2019. 5. J. Yosinski, J. Clune, A. Nguyen, T. Fuchs, and H. Lipson. Understanding Neural Networks Through Deep Visualization. In ICML Deep Learning Workshop, 2015 6. M. Kahng, P. Y. Andrews, A. Kalro, and D. H. Chau. ActiVis: Visual Exploration of Industry-Scale Deep Neural Network Models. IEEE Transactions on Visualization and Computer Graphics, 24(1):88–97, Jan. 2018. 7. https://cs231n.github.io/convolutional-networks/ 8. https://www.analyticsvidhya.com/blog/2020/02/learn-imageclassification-cnn-convolutional-neural-networks-3-datasets/ 9. https://towardsdatascience.com/understanding-cnn-convolutionalneural- network-69fd626ee7d4 10. https://medium.com/@birdortyedi_23820/deep-learning-lab-episode-2- cifar- 10-631aea84f11e 11. J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, and T. Chen. Recent advances in convolutional neural networks. Pattern Recognition, 77:354–377, May 2018. 12. Hamid, Y., Shah, F.A. and Sugumaram, M. (2014), ―Wavelet neural network model for network intrusion detection system‖, International Journal of Information Technology, Vol. 11 No. 2, pp. 251-263 13. G Sreeram , S Pradeep, K SrinivasRao , B.Deevan Raju , Parveen Nikhat , ― Moving ridge neuronal espionage network simulation for reticulum invasion sensing‖. International Journal of Pervasive Computing and Communications.https://doi.org/10.1108/IJPCC-05- 2020-0036 14. E. Stevens, L. Antiga, and T. Viehmann. Deep Learning with PyTorch. O’Reilly Media, 2019. 15. J. Yosinski, J. Clune, A. Nguyen, T. Fuchs, and H. Lipson. Understanding Neural Networks Through Deep Visualization. In ICML Deep Learning Workshop, 2015. 16. Aman Dureja, Payal Pahwa, ―Analysis of Non-Linear Activation Functions for Classification Tasks Using Convolutional Neural Networks‖, Recent Advances in Computer Science , Vol 2, Issue 3, 2019 ,PP-156-161 17. https://missinglink.ai/guides/neural-network-concepts/7-types-neuralnetwork-activation-functions-right/

scholarly journals Solving parametric PDE problems with artificial neural networks

2020 ◽  
pp. 1-15
Author(s):  
YUEHAW KHOO ◽  
JIANFENG LU ◽  
LEXING YING
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Evolution ◽  
Random Coefficients ◽  
Numerical Partial Differential Equations ◽  
The Neural Network ◽  
Physical Quantities

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modelled into the equations as random coefficients. However, very often the variability of physical quantities derived from PDE can be captured by a few features on the space of the coefficient fields. Based on such observation, we propose using neural network to parameterise the physical quantity of interest as a function of input coefficients. The representability of such quantity using a neural network can be justified by viewing the neural network as performing time evolution to find the solutions to the PDE. We further demonstrate the simplicity and accuracy of the approach through notable examples of PDEs in engineering and physics.

Identification of Thoracic Diseases by Exploiting Deep Neural Networks (Preprint)

2020 ◽  
Author(s):  
Albahli Saleh ◽  
Ali Alkhalifah
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Convolutional Neural Network ◽  
Deep Neural Networks ◽  
Medical Image Analysis ◽  
Medical Community ◽  
Learning Models ◽  
X Ray ◽  
Chest Disease

BACKGROUND To diagnose cardiothoracic diseases, a chest x-ray (CXR) is examined by a radiologist. As more people get affected, doctors are becoming scarce especially in developing countries. However, with the advent of image processing tools, the task of diagnosing these cardiothoracic diseases has seen great progress. A lot of researchers have put in work to see how the problems associated with medical images can be mitigated by using neural networks. OBJECTIVE Previous works used state-of-the-art techniques and got effective results with one or two cardiothoracic diseases but could lead to misclassification. In our work, we adopted GANs to synthesize the chest radiograph (CXR) to augment the training set on multiple cardiothoracic diseases to efficiently diagnose the chest diseases in different classes as shown in Figure 1. In this regard, our major contributions are classifying various cardiothoracic diseases to detect a specific chest disease based on CXR, use the advantage of GANs to overcome the shortages of small training datasets, address the problem of imbalanced data; and implementing optimal deep neural network architecture with different hyper-parameters to improve the model with the best accuracy. METHODS For this research, we are not building a model from scratch due to computational restraints as they require very high-end computers. Rather, we use a Convolutional Neural Network (CNN) as a class of deep neural networks to propose a generative adversarial network (GAN) -based model to generate synthetic data for training the data as the amount of the data is limited. We will use pre-trained models which are models that were trained on a large benchmark dataset to solve a problem similar to the one we want to solve. For example, the ResNet-152 model we used was initially trained on the ImageNet dataset. RESULTS After successful training and validation of the models we developed, ResNet-152 with image augmentation proved to be the best model for the automatic detection of cardiothoracic disease. However, one of the main problems associated with radiographic deep learning projects and research is the scarcity and unavailability of enough datasets which is a key component of all deep learning models as they require a lot of data for training. This is the reason why some of our models had image augmentation to increase the number of images without duplication. As more data are collected in the field of chest radiology, the models could be retrained to improve the accuracies of the models as deep learning models improve with more data. CONCLUSIONS This research employs the advantages of computer vision and medical image analysis to develop an automated model that has the clinical potential for early detection of the disease. Using deep learning models, the research aims to evaluate the effectiveness and accuracy of different convolutional neural network models in the automatic diagnosis of cardiothoracic diseases from x-ray images compared to diagnosis by experts in the medical community.

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