5 papers
Least-Squares Neural Network (LSNN) Method for Scalar Hyperbolic Partial Differential Equations
Min Liu, Zhiqiang Cai
This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differen…
A Structure-Guided Gauss-Newton Method for Shallow ReLU Neural Network
Zhiqiang Cai, Tong Ding, Min Liu +2
In this paper, we propose a structure-guided Gauss-Newton (SgGN) method for solving least squares problems using a shallow ReLU neural network. The method effectively takes advanta…
ReLU neural network approximation to piecewise constant functions
Zhiqiang Cai, Junpyo Choi, Min Liu
This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in . Under the…
Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps
Zhiqiang Cai, Junpyo Choi, Min Liu
The least-squares ReLU neural network (LSNN) method was introduced and studied for solving linear advection-reaction equation with discontinuous solution in \cite{Cai2021linear,cai…
Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Discontinuity Interface
Zhiqiang Cai, Junpyo Choi, Min Liu
We studied the least-squares ReLU neural network (LSNN) method for solving linear advection-reaction equation with discontinuous solution in [Cai, Zhiqiang, Jingshuang Chen, and Mi…