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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

Computer methods in applied mechanics and engineering, 2021-12, Vol.387, p.114129, Article 114129

2021

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A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

Journal of computational physics, 2021-06, Vol.435, p.110242, Article 110242

2021

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A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

Journal of computational physics, 2020-03, Vol.404, p.109121, Article 109121

2020

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On computing the hyperparameter of extreme learning machines: Algorithm and application to computational PDEs, and comparison with classical and high-order finite elements

Journal of computational physics, 2022-08, Vol.463, p.111290, Article 111290

2022

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An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices

Journal of computational physics, 2019-09, Vol.393, p.229-257

2019

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A modified batch intrinsic plasticity method for pre-training the random coefficients of extreme learning machines

Journal of computational physics, 2021-11, Vol.445, p.110585, Article 110585

2021

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A method for computing inverse parametric PDE problems with random-weight neural networks

Journal of computational physics, 2023-09, Vol.489, p.112263, Article 112263

2023

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Numerical approximation of partial differential equations by a variable projection method with artificial neural networks

Computer methods in applied mechanics and engineering, 2022-08, Vol.398, p.115284, Article 115284

2022

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An extreme learning machine-based method for computational PDEs in higher dimensions

Computer methods in applied mechanics and engineering, 2024-01, Vol.418, p.116578, Article 116578

2024

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Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Journal of computational physics, 2019-07, Vol.388, p.1-22

2019

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Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm

Journal of computational physics, 2018-08, Vol.366, p.33-70

2018

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Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine

Journal of scientific computing, 2023-05, Vol.95 (2), p.35, Article 35

2023

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A family of second-order energy-stable schemes for Cahn–Hilliard type equations

Journal of computational physics, 2019-04, Vol.383, p.24-54

2019

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Local randomized neural networks with discontinuous Galerkin methods for partial differential equations

Journal of computational and applied mathematics, 2024-08, Vol.445, Article 115830

2024

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Flow past a trapezoidal tab

Journal of fluid mechanics, 2004-07, Vol.510, p.219-242

2004

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A gPAV-based unconditionally energy-stable scheme for incompressible flows with outflow/open boundaries

Computer methods in applied mechanics and engineering, 2020-06, Vol.365, p.112969, Article 112969

2020

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On a simple and effective thermal open boundary condition for convective heat transfer problems

International journal of heat and mass transfer, 2020-04, Vol.151, p.119355, Article 119355

2020

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Energy-stable boundary conditions based on a quadratic form: Applications to outflow/open-boundary problems in incompressible flows

Journal of computational physics, 2019-08, Vol.391, p.179-215

2019

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Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms

Journal of computational physics, 2023-12, Vol.495, p.112527, Article 112527

2023

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Turbulent drag reduction by constant near-wall forcing

Journal of fluid mechanics, 2007-07, Vol.582, p.79-101

2007

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An energy-stable scheme for incompressible Navier-Stokes equations with periodically updated coefficient matrix

Journal of computational physics, 2020-10, Vol.418, p.109624, Article 109624

2020

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Cross-site computations on the TeraGrid

Computing in science & engineering, 2005-09, Vol.7 (5), p.14-23

2005

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A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio

Journal of computational physics, 2019-11, Vol.397, p.108832, Article 108832

2019

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Gold-implanted plasmonic quartz plate as a launch pad for laser-driven photoacoustic microfluidic pumps

Proceedings of the National Academy of Sciences - PNAS, 2019-04, Vol.116 (14), p.6580-6585

2019

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Spectral distributed Lagrange multiplier method: algorithm and benchmark tests

Journal of computational physics, 2004-04, Vol.195 (2), p.695-717

2004

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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks

A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity

On computing the hyperparameter of extreme learning machines: Algorithm and application to computational PDEs, and comparison with classical and high-order finite elements

An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices

A modified batch intrinsic plasticity method for pre-training the random coefficients of extreme learning machines

A method for computing inverse parametric PDE problems with random-weight neural networks

Numerical approximation of partial differential equations by a variable projection method with artificial neural networks

An extreme learning machine-based method for computational PDEs in higher dimensions

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Multiphase flows of N immiscible incompressible fluids: An outflow/open boundary condition and algorithm

Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine

A family of second-order energy-stable schemes for Cahn–Hilliard type equations

Local randomized neural networks with discontinuous Galerkin methods for partial differential equations

Flow past a trapezoidal tab

A gPAV-based unconditionally energy-stable scheme for incompressible flows with outflow/open boundaries

On a simple and effective thermal open boundary condition for convective heat transfer problems

Energy-stable boundary conditions based on a quadratic form: Applications to outflow/open-boundary problems in incompressible flows

Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: Error analysis and algorithms

Turbulent drag reduction by constant near-wall forcing

An energy-stable scheme for incompressible Navier-Stokes equations with periodically updated coefficient matrix

Cross-site computations on the TeraGrid

A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio

Gold-implanted plasmonic quartz plate as a launch pad for laser-driven photoacoustic microfluidic pumps

Spectral distributed Lagrange multiplier method: algorithm and benchmark tests

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