115 citations · 178 across the 6 of their papers we have counts for
6 papers
Least-Squares Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Laws: Discrete Divergence Operator
Zhiqiang Cai, Jingshuang Chen, Min Liu
A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equiva…
Self-adaptive deep neural network: Numerical approximation to functions and PDEs
Zhiqiang Cai, Jingshuang Chen, Min Liu
Designing an optimal deep neural network for a given task is important and challenging in many machine learning applications. To address this issue, we introduce a self-adaptive al…
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…
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
Zhiqiang Cai, Jingshuang Chen, Min Liu +1
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to ap…