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George Em Karniadakis

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Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs

Journal Article

Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs

Communications in Computational Physics, Vol. 34 (2023), Iss. 4 : pp. 1133–1176

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Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Journal Article

Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Communications in Computational Physics, Vol. 31 (2022), Iss. 2 : pp. 331–369

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Dying ReLU and Initialization: Theory and Numerical Examples

Journal Article

Dying ReLU and Initialization: Theory and Numerical Examples

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 1671–1706

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Journal Article

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2002–2041

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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Journal Article

On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs

Communications in Computational Physics, Vol. 28 (2020), Iss. 5 : pp. 2042–2074

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Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

Journal Article

Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 4 : pp. 876–902

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