115 citations · 220 across the 19 of their papers we have counts for
5 papers · 1 filter
Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations
Difeng Cai, Zhiqiang Cai
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an expli…
Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs
Min Liu, Zhiqiang Cai
In this paper, we study adaptive neuron enhancement (ANE) method for solving self-adjoint second-order elliptic partial differential equations (PDEs). The ANE method is a self-adap…
Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation
Min Liu, Zhiqiang Cai, Jingshuang Chen
In this paper, we introduce adaptive neuron enhancement (ANE) method for the best least-squares approximation using two-layer ReLU neural networks (NNs). For a given function f(x),…
Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation
Zhiqiang Cai, Jingshuang Chen, Min Liu
This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution. The method is a discretization of an equi…
Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law
Zhiqiang Cai, Jingshuang Chen, Min Liu
We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperfor…