Related papers: A practical PINN framework for multi-scale problem…

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Singular regular points often arise in differential equations describing physical phenomena such as fluid dynamics, electromagnetism, and gravitation. Traditional numerical techniques often fail or become unstable near these points,…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

The gravitational collapse of a massless scalar field remains a demanding benchmark for numerical methods in numerical relativity, as it exhibits critical behavior at the boundary between dispersion and black hole formation. In this work we…

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

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…

Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process, making them well-suited for solving complex scientific and engineering problems. Recently,…

Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in…