Related papers: Benchmarking Physics-Informed Neural Networks and …
Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which…
Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators…
Solving for the frequency-domain scattered wavefield via physics-informed neural network (PINN) has great potential in seismic modeling and inversion. However, when dealing with high-frequency wavefields, its accuracy and training cost…
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…
Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has…
Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…
Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…
Mode conversion in non-homogeneous elastic media makes it challenging to interpret physical properties accurately. Decomposing these modes correctly is crucial across various scientific areas. Recent machine learning approaches have been…
In this paper, a novel hybrid method based on the finite element method (FEM) and physics-informed kernel function neural networks (PIKFNNs) is proposed and applied to the prediction of underwater acoustic propagation induced by structural…
Neutrino oscillations provide crucial insights into fundamental particle physics, with two-flavor approximations effectively describing reactor and atmospheric phenomena. This paper investigates the application of Physics-Informed Neural…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…
Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…
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…
Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
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…
PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…
Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…