Related papers: Physics-Informed Neural Networks for Weakly Compre…
In this paper, a modified version of conservative Physics-informed Neural Networks (cPINN for short) is provided to construct the weak solutions of Riemann problem for the hyperbolic scalar conservation laws in non-conservative form. To…
Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…
The main focus of this paper is to analyze the behavior of a numerical solution of the Timoshenko system coupled with Thermoelasticity and incorporating second sound effects. In order to address this target, we employ the Physics-Informed…
In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture…
Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…
Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced…
Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to…
Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…
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…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…
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) 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…
This study enhances the application of Physics-Informed Neural Networks (PINNs) for modeling discontinuous solutions in both hydrodynamics and relativistic hydrodynamics. Conventional PINNs, trained with partial differential equation…
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…
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…
We construct in this article the semi-analytic Physics Informed Neural Networks (PINNs), called {\em singular layer PINNs} (or {\em sl-PINNs}), that are suitable to predict the stiff solutions of plane-parallel flows at a small viscosity.…
Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical…
In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids bearing different material properties, are separated by a…
Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning,…