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

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Newton's method leverages curvature information to boost performance, and thus outperforms first-order methods for distributed learning problems. However, Newton's method is not practical in large-scale and heterogeneous learning…

Cognitive Autonomous Networks (CAN) deploys learning based Cognitive Functions (CF) instead of conventional rule-based SON Functions (SF) as Network Automation Functions (NAF) to increase the system autonomy. These CFs work in parallel…

We present several key advances to the Physics and Equality Constrained Artificial Neural Networks (PECANN) framework, substantially improving its capacity to solve challenging partial differential equations (PDEs). Our enhancements broaden…

A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…

We propose a novel deep learning (DL) approach to solve one-dimensional non-linear elliptic, parabolic, and hyperbolic problems on graphs. A system of physics-informed neural network (PINN) models is used to solve the differential…

Purpose: We seek to use neural networks (NNs) to solve a well-known system of differential equations describing the balance between T cells and HIV viral burden. Materials and Methods: In this paper, we employ a 3-input parallel NN to…

In the data-driven world of actuarial science, machine learning (ML) plays a crucial role in predictive modeling, enhancing risk assessment and pricing strategies. Neural networks, specifically combined actuarial neural networks (CANN), are…

Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…

The customizable nature of deep learning models have allowed them to be successful predictors in various disciplines. These models are often trained with respect to thousands or millions of instances for complicated problems, but the…

Deep convolutional neural networks (CNNs) have shown excellent performance in object recognition tasks and dense classification problems such as semantic segmentation. However, training deep neural networks on large and sparse datasets is…

In this work, we use the artificial neural network (ANN) method to study and predict the distribution of strong coupling constants by fitting the existing data. Our approach takes advantage of the ability of ANN to learn complex nonlinear…

Despite recent advances in multi-scale deep representations, their limitations are attributed to expensive parameters and weak fusion modules. Hence, we propose an efficient approach to fuse multi-scale deep representations, called…

Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…

We will develop a nonlinear upscaling method for nonlinear transport equation. The proposed scheme gives a coarse scale equation for the cell average of the solution. In order to compute the parameters in the coarse scale equation, a local…

We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and…

Anomaly detection is a significant and hence well-studied problem. However, developing effective anomaly detection methods for complex and high-dimensional data remains a challenge. As Generative Adversarial Networks (GANs) are able to…

The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…

In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…