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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...
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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...
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01/27/2023
Adaptive Least-Squares Methods for Convection-Dominated Diffusion-Reaction Problems
This paper studies adaptive least-squares finite element methods for con...
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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...
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09/09/2022
Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network
Adaptive training methods for physical-informed neural network (PINN) re...
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11/19/2021
Learn Quasi-stationary Distributions of Finite State Markov Chain
We propose a reinforcement learning (RL) approach to compute the express...
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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...
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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...
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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...
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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...
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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...
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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 ...
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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...
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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 ...
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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...
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02/12/2016