Related papers: KP-PINNs: Kernel Packet Accelerated Physics Inform…

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…

Physics informed neural networks (PINNs) have drawn attention in recent years in engineering problems due to their effectiveness and ability to tackle the problems without generating complex meshes. PINNs use automatic differentiation to…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

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…

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…

In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of…

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for…

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…

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) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons…

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…