Related papers: Singular Layer Physics-Informed Neural Network Met…
Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann electrostatics. These problems are characterized by sharp…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…
Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…
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"…
Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…
In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…
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…
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) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…
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…
We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…
In this paper, we investigate several techniques for modeling the one-dimensional advection equation for a specific class of problems with discontinuous initial and boundary conditions using physics-informed neural networks (PINNs). To…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
Although Physics-Informed Neural Networks (PINNs) have been successfully applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging…
With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…
We propose a hybrid solver that fuses the dimensionality-reduction strengths of the Method of Lines (MOL) with the flexibility of Physics-Informed Neural Networks (PINNs). Instead of approximating spatial derivatives with fixed…