相关论文: Deep Learning solutions to singular ordinary diffe…

Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and…

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

To expand on the burgeoning research on physics-informed neural networks (PINNs) and their ability to solve the eigenvalue problems in black hole (BH) perturbation theory, we implement a supervised learning approach to solve the…

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…

Since the introduction of deep learning for solving partial differential equations (PDEs), there has been growing interest in real-time system responses, where the kernel function plays a key role. Physics-informed neural networks (PINNs),…

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

We introduce a Physics-Informed Neural Networks(PINN) to solve a relativistic Burgers equation in the exterior domain of a Schwarzschild black hole. Our main contribution is a PINN architecture that is able to simulate shock wave formations…

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…

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equations, and their coupled forms in both one and two-dimensional…

Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

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…

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…

The measurement of black hole spin is considered one of the key problems in relativistic astrophysics. Existing methods, such as continuum fitting, X-ray reflection spectroscopy and quasi-periodic oscillation analysis, have systematic…

Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…