Related papers: Multi-level Neural Networks for high-dimensional p…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…

This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Convolutional Neural Networks (CNNs) have been successfully utilized in the medical diagnosis of many illnesses. Nevertheless, identifying the optimal architecture and hyperparameters among the available possibilities might be a substantial…

Traditional architectures for solving computer vision problems and the degree of success they enjoyed have been heavily reliant on hand-crafted features. However, of late, deep learning techniques have offered a compelling alternative --…

Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of 'what' and…

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…

The growing complexity of machinery and the increasing demand for operational efficiency and safety have driven the development of advanced fault diagnosis techniques. Among these, convolutional neural networks (CNNs) have emerged as a…

The field of machine learning has taken a dramatic twist in recent times, with the rise of the Artificial Neural Network (ANN). These biologically inspired computational models are able to far exceed the performance of previous forms of…

Important advances have been made using convolutional neural network (CNN) approaches to solve complicated problems in areas that rely on grid structured data such as image processing and object classification. Recently, research on graph…

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level…

Convolutional Neural Networks (CNNs) have been successfully applied to many computer vision tasks, such as image classification. By performing linear combinations and element-wise nonlinear operations, these networks can be thought of as…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…