Related papers: Multi evolutional deep neural networks (Multi-EDNN…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Information networks are ubiquitous and are ideal for modeling relational data. Networks being sparse and irregular, network embedding algorithms have caught the attention of many researchers, who came up with numerous embeddings algorithms…

Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…

As a fundamental mathmatical tool in many engineering disciplines, coupled differential equation groups are being widely used to model complex structures containing multiple physical quantities. Engineers constantly adjust structural…

This paper presents a novel Energy-Equidistributed adaptive sampling framework for multi-dimensional conservative PDEs, introducing both location-based and velocity-based formulations of Energy-Equidistributed moving mesh PDEs (EMMPDEs).…

This paper presents a deep learning approach for the classification of Engineering (CAD) models using Convolutional Neural Networks (CNNs). Owing to the availability of large annotated datasets and also enough computational power in the…

Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…

As a promising framework for resolving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have received widespread attention from industrial and scientific fields. However, lack of expressive ability and…

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…

Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional…

Both the Dictionary Learning (DL) and Convolutional Neural Networks (CNN) are powerful image representation learning systems based on different mechanisms and principles, however whether we can seamlessly integrate them to improve the…

In real applications, different computation-resource devices need different-depth networks (e.g., ResNet-18/34/50) with high-accuracy. Usually, existing methods either design multiple networks and train them independently, or construct…

Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme…

While neural networks for learning representation of multi-view data have been previously proposed as one of the state-of-the-art multi-view dimension reduction techniques, how to make the representation discriminative with only a small…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…