Related papers: RBF-MGN:Solving spatiotemporal PDEs with Physics-i…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great…

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

Physics--informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct…

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…

Physics-Informed Neural Networks (PINNs) have been widely used for solving partial differential equations (PDEs) of different types, including fractional PDEs (fPDES) [29]. Herein, we propose a new general (quasi) Monte Carlo PINN for…

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

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…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

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…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

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…

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…