Related papers: PMNN:Physical Model-driven Neural Network for solv…

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

We have developed a novel differential equation solver software called PND based on the physics-informed neural network for molecular dynamics simulators. Based on automatic differentiation technique provided by Pytorch, our software allows…

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to…

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…

The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters,…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus…

Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems modeled by Partial Differential Equations (PDEs). This paper introduces IDRLnet, a Python toolbox for modeling and…

This paper proposed a novel radial basis function neural network (RBFNN) to solve various partial differential equations (PDEs). In the proposed RBF neural networks, the physics-informed kernel functions (PIKFs), which are derived according…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

As deep neural networks (DNNs) become deeper, the training time increases. In this perspective, multi-GPU parallel computing has become a key tool in accelerating the training of DNNs. In this paper, we introduce a novel methodology to…

In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informed neural networks. They solve forward and inverse problems…

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time. In the first inverse problem, we…

Spiking Neural Networks (SNNs) hold great potential to realize brain-inspired, energy-efficient computational systems. However, current SNNs still fall short in terms of multi-scale temporal processing compared to their biological…

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…