Zhiqiang Cai | DeepAI

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Featured Co-authors

Jie Tang
135 publications
Jing Yang
111 publications
Min Liu
62 publications
Xiang Zhou
53 publications
Shun Zhang
37 publications
Xinyu Liu
25 publications
Tai Wang
20 publications
Cuiyu He
9 publications
Karthik Ramani
7 publications
Jingshuang Chen
6 publications
Difeng Cai
5 publications

∙ 06/12/2023

Least-Squares Neural Network (LSNN) Method For Linear Advection-Reaction Equation: Non-constant Jumps

The least-squares ReLU neural network method (LSNN) was introduced and s...

0 Zhiqiang Cai, et al. ∙

∙ 05/24/2023

Deep Ritz Method with Adaptive Quadrature for Linear Elasticity

In this paper, we study the deep Ritz method for solving the linear elas...

0 Min Liu, et al. ∙

∙ 01/27/2023

Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems

This paper studies adaptive least-squares finite element methods for con...

0 Zhiqiang Cai, et al. ∙

∙ 01/15/2023

Least-Squares Neural Network (LSNN) Method for Linear Advection-Reaction Equation: General Discontinuous Interface

We studied the least-squares ReLU neural network method (LSNN) for solvi...

0 Zhiqiang Cai, et al. ∙

∙ 09/09/2022

Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network

Adaptive training methods for physical-informed neural network (PINN) re...

0 Jiayue Han, et al. ∙

∙ 11/19/2021

Learn Quasi-stationary Distributions of Finite State Markov Chain

We propose a reinforcement learning (RL) approach to compute the express...

0 Zhiqiang Cai, et al. ∙

∙ 10/21/2021

Finite Volume Least-Squares Neural Network (FV-LSNN) Method for Scalar Nonlinear Hyperbolic Conservation Laws

In [4], we introduced the least-squares ReLU neural network (LSNN) metho...

0 Zhiqiang Cai, et al. ∙

∙ 09/07/2021

Self-adaptive deep neural network: Numerical approximation to functions and PDEs

Designing an optimal deep neural network for a given task is important a...

0 Zhiqiang Cai, et al. ∙

∙ 07/19/2021

Adaptive Two-Layer ReLU Neural Network: I. Best Least-squares Approximation

In this paper, we introduce adaptive neuron enhancement (ANE) method for...

0 Min Liu, et al. ∙

∙ 07/14/2021

Adaptive Two-Layer ReLU Neural Network: II. Ritz Approximation to Elliptic PDEs

In this paper, we study adaptive neuron enhancement (ANE) method for sol...

0 Min Liu, et al. ∙

∙ 07/13/2021

Hybrid A Posteriori Error Estimators for Conforming Finite Element Approximations to Stationary Convection-Diffusion-Reaction equations

We consider the a posteriori error estimation for convection-diffusion-r...

0 Difeng Cai, et al. ∙

∙ 05/25/2021

Least-Squares ReLU Neural Network (LSNN) Method For Linear Advection-Reaction Equation

This paper studies least-squares ReLU neural network method for solving ...

0 Zhiqiang Cai, et al. ∙

∙ 05/25/2021

Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law

We introduced the least-squares ReLU neural network (LSNN) method for so...

0 Zhiqiang Cai, et al. ∙

∙ 01/24/2020

Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements

The well-known Prager-Synge identity is valid in H^1(Ω) and serves as a ...

0 Cuiyu He, et al. ∙

∙ 11/05/2019

Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs

This paper studies an unsupervised deep learning-based numerical approac...

23 Zhiqiang Cai, et al. ∙

∙ 02/12/2016

An Empirical Study on Academic Commentary and Its Implications on Reading and Writing

The relationship between reading and writing (RRW) is one of the major t...

0 Tai Wang, et al. ∙

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