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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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