We study a family of $ H^ m $-conforming piecewise polynomials based on artificial neural
network, named as the finite neuron method (FNM), for numerical solution of $2 m $-th order …

Recently, neural networks have been widely applied for solving partial differential equations
(PDEs). Although such methods have been proven remarkably successful on practical …

This paper develops a gradient descent (GD) method for solving a system of nonlinear
equations with an explicit formulation. We theoretically prove that the GD method has linear …

Recently, neural networks have been widely applied for solving partial differential equations
(PDEs). Although such methods have been proven remarkably successful on practical …

The numerical solution of differential equations using machine learning-based approaches
has gained significant popularity. Neural network-based discretization has emerged as a …

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs)
in the applications of physics, biology, and engineering. One effective approach for solving …

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for
understanding tumor growth dynamics and designing personalized radiotherapy treatment …

We present a novel and mathematically transparent approach to function approximation and
the training of large, high-dimensional neural networks, based on the approximate least …

This paper introduces Residual-based Smote (RSmote), an innovative local adaptive
sampling technique tailored to improve the performance of Physics-Informed Neural …

The article focuses on using randomized neural networks (RNNs) to solve obstacle
problems, which are elliptic variational inequalities. Topics include the application of RNNs …