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09/13/2023
An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions
We present two effective methods for solving high-dimensional partial di...
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05/15/2023
Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows
We develop a method for modeling and simulating a class of two-phase flo...
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03/22/2023
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time
We consider the approximation of a class of dynamic partial differential...
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10/09/2022
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks
We present a method for computing the inverse parameters and the solutio...
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06/11/2022
Local Randomized Neural Networks with Discontinuous Galerkin Methods for Partial Differential Equations
Randomized neural networks (RNN) are a variation of neural networks in w...
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04/24/2022
Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine
The extreme learning machine (ELM) method can yield highly accurate solu...
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01/24/2022
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks
We present a method for solving linear and nonlinear PDEs based on the v...
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10/27/2021
On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements
We consider the use of extreme learning machines (ELM) for computational...
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03/14/2021
A Modified Batch Intrinsic Plasticity Method for Pre-training the Random Coefficients of Extreme Learning Machines
In extreme learning machines (ELM) the hidden-layer coefficients are ran...
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12/04/2020
Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equations
We present a neural network-based method for solving linear and nonlinea...
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07/15/2020
A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks
We present a simple and effective method for representing periodic funct...
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06/14/2020
gPAV-Based Unconditionally Energy-Stable Schemes for the Cahn-Hilliard Equation: Stability and Error Analysis
We present several first-order and second-order numerical schemes for th...
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03/30/2019