Related papers: Physics-Informed Neural Networks for Nonlocal Beam…

The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically…

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes, which require knowledge about the appearing…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

We study the training and performance of physics-informed learning for initial and boundary value problems (IBVP) with physics-informed neural networks (PINNs) from a statistical learning perspective. Specifically, we restrict ourselves to…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in…

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…

This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving partial differential equations~(PDEs) in various scientific and engineering domains. However, traditional PINN architectures typically rely on large, fully…