Abstract—Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the exact satisfaction of the boundary conditions. The method has been successfully tested on two-dimensional and three-dimensional PDEs and has yielded accurate results. Index Terms—Boundary value...
This book introduces a variety of neural network methods for solving differential equations arising ...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
This paper reports a new numerical method based on radial basis function net-works (RBFNs) for solvi...
We present a method to solve initial and boundary value problems using artificial neural networks. A...
Recently deep learning surrogates and neural operators have shown promise in solving partial differe...
Neural network-based approaches for solving partial differential equations (PDEs) have recently rece...
Various researchers have used one hidden layer neural networks (weighted sums of sigmoids) to find t...
Various researchers have used one hidden layer neural networks (weighted sums of sigmoids) to find t...
Ordinary Differential Equations (ODEs) play a key role in describing the physical, chemical, and bio...
he aim of this paper is to design neural network to present a method to solve Singular perturbation ...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
technique is presented to solve Partial Differential Equations (PDEs). The technique is based on con...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
This book introduces a variety of neural network methods for solving differential equations arising ...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
This paper reports a new numerical method based on radial basis function net-works (RBFNs) for solvi...
We present a method to solve initial and boundary value problems using artificial neural networks. A...
Recently deep learning surrogates and neural operators have shown promise in solving partial differe...
Neural network-based approaches for solving partial differential equations (PDEs) have recently rece...
Various researchers have used one hidden layer neural networks (weighted sums of sigmoids) to find t...
Various researchers have used one hidden layer neural networks (weighted sums of sigmoids) to find t...
Ordinary Differential Equations (ODEs) play a key role in describing the physical, chemical, and bio...
he aim of this paper is to design neural network to present a method to solve Singular perturbation ...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
technique is presented to solve Partial Differential Equations (PDEs). The technique is based on con...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
This book introduces a variety of neural network methods for solving differential equations arising ...
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN...
This paper reports a new numerical method based on radial basis function net-works (RBFNs) for solvi...