Related papers: Finite-PINN: A Physics-Informed Neural Network wit…
Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the…
Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This…
Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…
Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine…
We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…
Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…
Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely…
Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…
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…
Accurate modeling of closure terms is a critical challenge in engineering and scientific research, particularly when data is sparse (scarse or incomplete), making widely applicable models difficult to develop. This study proposes a novel…
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…
In this study, we present a novel computational framework that integrates the finite volume method with graph neural networks to address the challenges in Physics-Informed Neural Networks(PINNs). Our approach leverages the flexibility of…
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…
In this work, a physics-informed neural networks (PINNs) based algorithm is used for simulation of nonlinear 1D and 2D Burgers' type models. This scheme relies on a neural network built to approximate the problem solution and use a trial…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics-informed neural networks (PINNs). Specifically, we illustrate how…
Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…