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In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Physics Informed Neural Networks (PINNs) often exhibit failure modes in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep…

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

The use of neural networks to solve differential equations, as an alternative to traditional numerical solvers, has increased recently. However, error bounds for the obtained solutions have only been developed for certain equations. In this…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for analyzing nonlinear partial differential equations and identifying governing equations from observational data. In this study, we apply PINNs to investigate…

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…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs), particularly in regimes where labeled data are scarce and physical constraints can be…

Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…