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In this paper, we study the linear transport model by adopting the deep learning method, in particular the deep neural network (DNN) approach. While the interest of using DNN to study partial differential equations is arising, here we adapt…

We present a novel method for cell segmentation in microscopy images which is inspired by the Generative Adversarial Neural Network (GAN) approach. Our framework is built on a pair of two competitive artificial neural networks, with a…

Over one in three people are affected by neurodegenerative disorders. Neural stem cells, which are multipotent regenerative cells with the potential to differentiate into any of the neural cell types, have immense therapeutic potential for…

The recent surge in popularity of deep generative models for 3D objects has highlighted the need for more efficient training methods, particularly given the difficulties associated with training with conventional 3D representations, such as…

For image classification problems, various neural network models are commonly used due to their success in yielding high accuracies. Convolutional Neural Network (CNN) is one of the most frequently used deep learning methods for image…

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…

We introduce CAN, a simple, efficient and scalable method for self-supervised learning of visual representations. Our framework is a minimal and conceptually clean synthesis of (C) contrastive learning, (A) masked autoencoders, and (N) the…

Deep Neural Network (DNN) based super-resolution algorithms have greatly improved the quality of the generated images. However, these algorithms often yield significant artifacts when dealing with real-world super-resolution problems due to…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…

Solving general high-dimensional partial differential equations (PDE) is a long-standing challenge in numerical mathematics. In this paper, we propose a novel approach to solve high-dimensional linear and nonlinear PDEs defined on arbitrary…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Maxwell's equations govern light propagation and its interaction with matter. Therefore, the solution of Maxwell's equations using computational electromagnetic simulations plays a critical role in understanding light-matter interaction and…

Conventional predictive Artificial Neural Networks (ANNs) commonly employ deterministic weight matrices; therefore, their prediction is a point estimate. Such a deterministic nature in ANNs causes the limitations of using ANNs for medical…

Automated design methods for convolutional neural networks (CNNs) have recently been developed in order to increase the design productivity. We propose a neuroevolution method capable of evolving and optimizing CNNs with respect to the…

In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

The method of choice for parameter aggregation in Deep Neural Network (DNN) training, a network-intensive task, is shifting from the Parameter Server model to decentralized aggregation schemes (AllReduce) inspired by theoretical guarantees…