Related papers: KP-PINNs: Kernel Packet Accelerated Physics Inform…
Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…
This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more…
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…
The automatic differentiation (AD) in the vanilla physics-informed neural networks (PINNs) is the computational bottleneck for the high-efficiency analysis. The concept of derivative discretization in smoothed particle hydrodynamics (SPH)…
Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…
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…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…
In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…
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…
Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…
Physics-informed neural networks (PINNs) have attracted a lot of attention in scientific computing as their functional representation of partial differential equation (PDE) solutions offers flexibility and accuracy features. However, their…
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions…
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…
Physics-informed neural networks (PINNs) have gained prominence for their capability to tackle supervised learning tasks that conform to physical laws, notably nonlinear partial differential equations (PDEs). This paper presents…
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to…
Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…