Close Search Advanced
Journals
Resources
About Us
Open Access
Journals
Resources
About Us
Open Access

All Journals

Xiliang Lu

Results

Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

Journal Article

Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 239–263

Info
The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

Journal Article

The Discontinuous Galerkin Method by Patch Reconstruction for Helmholtz Problems

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 1 : pp. 30–48

Info
An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

Journal Article

An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 1 : pp. 1–18

Info
Convergence Rate Analysis for Deep Ritz Method

Journal Article

Convergence Rate Analysis for Deep Ritz Method

Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1020–1048

Info
A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

Journal Article

A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs

Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1272–1295

Info
Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm

Journal Article

Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm

Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 190–209

Info
Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Condition

Journal Article

Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Condition

CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 4 : pp. 761–791

Info
An Efficient Variational Model for Multiplicative Noise Removal

Journal Article

An Efficient Variational Model for Multiplicative Noise Removal

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 1 : pp. 125–140

Info
Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

Journal Article

Improved Analysis of PINNs: Alleviate the CoD for Compositional Solutions

Annals of Applied Mathematics, Vol. 39 (2023), Iss. 3 : pp. 239–263

Info
Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

Journal Article

Error Analysis of the Nonconforming $P_1$ Finite Element Method to the Sequential Regularization Formulation for Unsteady Navier-Stokes Equations

Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 43–70

Info
Convergence Analysis for Over-Parameterized Deep Learning

Journal Article

Convergence Analysis for Over-Parameterized Deep Learning

Communications in Computational Physics, Vol. 36 (2024), Iss. 1 : pp. 71–103

Info
Analysis of Deep Ritz Methods for Semilinear Elliptic Equations

Journal Article

Analysis of Deep Ritz Methods for Semilinear Elliptic Equations

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 1 : pp. 181–209

Info