Related papers: Cell-average based neural network method for high …

Physics and equality constrained artificial neural networks (PECANN) are grounded in methods of constrained optimization to properly constrain the solution of partial differential equations (PDEs) with their boundary and initial conditions…

Recent works have shown that deep neural networks can achieve super-human performance in a wide range of image classification tasks in the medical imaging domain. However, these works have primarily focused on classification accuracy,…

In this paper, we aim at developing scalable neural network-type learning systems. Motivated by the idea of "constructive neural networks" in approximation theory, we focus on "constructing" rather than "training" feed-forward neural…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

We introduce a new method, called CNNAS (convolutional neural networks for atomistic systems), for calculating the total energy of atomic systems which rivals the computational cost of empirical potentials while maintaining the accuracy of…

Class imbalance occurs in many real-world applications, including image classification, where the number of images in each class differs significantly. With imbalanced data, the generative adversarial networks (GANs) leans to majority class…

The Convolutional Neural Network (CNN) has shown impressive performance in image classification because of its strong learning capabilities. However, it demands a substantial and balanced dataset for effective training. Otherwise, networks…

Pixel-level labelling tasks, such as semantic segmentation, play a central role in image understanding. Recent approaches have attempted to harness the capabilities of deep learning techniques for image recognition to tackle pixel-level…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…

This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and…

Solar energy is one of the most dependable renewable energy technologies, as it is feasible almost everywhere globally. However, improving the efficiency of a solar PV system remains a significant challenge. To enhance the robustness of the…

In this paper, we propose a general dual convolutional neural network (DualCNN) for low-level vision problems, e.g., super-resolution, edge-preserving filtering, deraining and dehazing. These problems usually involve the estimation of two…

Nature has always been our inspiration in the research, design and development of materials and has driven us to gain a deep understanding of the mechanisms that characterize anisotropy and inelastic behavior. All this knowledge has been…

Inspired by the Kolmogorov-Arnold representation theorem, KANs offer a novel framework for function approximation by replacing traditional neural network weights with learnable univariate functions. This design demonstrates significant…

In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep…

Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…

The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…

Solving nonlinear algebraic equations is a fundamental but challenging problem in scientific computations and also has many applications in system engineering. Though traditional iterative methods and modern optimization algorithms have…

Artificial neural networks (ANNs) have been successfully applied to solve a variety of classification and function approximation problems. Although ANNs can generally predict better than decision trees for pattern classification problems,…