230 citations · 1.3k across the 27 of their papers we have counts for
28 papers
Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows
Jielin Yang, Ivan C. Christov, Suchuan Dong
We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed externa…
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time
Yanxia Qian, Yongchao Zhang, Yunqing Huang +1
We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide…
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks
Suchuan Dong, Yiran Wang
We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learn…
Local Randomized Neural Networks with Discontinuous Galerkin Methods for Partial Differential Equations
Jingbo Sun, Suchuan Dong, Fei Wang
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are o…
Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine
Naxian Ni, Suchuan Dong
The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the n…
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks
Suchuan Dong, Jielin Yang
We present a method for solving linear and nonlinear PDEs based on the variable projection (VarPro) framework and artificial neural networks (ANN). For linear PDEs, enforcing the b…