20 citations · 41 across the 11 of their papers we have counts for
11 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…
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…
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…
Evolving Neural Network (ENN) Method for One-Dimensional Scalar Hyperbolic Conservation Laws: I Linear and Quadratic Fluxes
Zhiqiang Cai, Brooke Hejnal
We propose and study the evolving neural network (ENN) method for solving one-dimensional scalar hyperbolic conservation laws with linear and quadratic spatial fluxes. The ENN meth…
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…
Deep Ritz Method with Adaptive Quadrature for Linear Elasticity
Min Liu, Zhiqiang Cai, Karthik Ramani
In this paper, we study the deep Ritz method for solving the linear elasticity equation from a numerical analysis perspective. A modified Ritz formulation using the …
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…
Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network
Jiayue Han, Zhiqiang Cai, Zhiyou Wu +1
Adaptive training methods for Physics-informed neural network (PINN) require dedicated constructions of the distribution of weights assigned at each training sample. To efficiently…
DDPG based on multi-scale strokes for financial time series trading strategy
Jun-Cheng Chen, Cong-Xiao Chen, Li-Juan Duan +1
With the development of artificial intelligence,more and more financial practitioners apply deep reinforcement learning to financial trading strategies.However,It is difficult to e…
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…