2 citations · 5 across the 13 of their papers we have counts for
8 papers · 1 filter
Multilevel Neural Corrections with Adaptive Sampling for Partial Differential Equations
Yu Yang, Qiaolin He
We propose a multi-level framework for deep neural PDE solvers that integrates adaptive sampling with additive neural corrections. At each level, an adaptive sampling distribution…
Adaptive feature capture method for solving partial differential equations with near singular solutions
Yangtao Deng, Qiaolin He, Xiaoping Wang
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh gene…
Runge-Kutta Random Feature Method for Solving Multiphase Flow Problems of Cells
Yangtao Deng, Qiaolin He
Cell collective migration plays a crucial role in a variety of physiological processes. In this work, we propose the Runge-Kutta random feature method to solve the nonlinear and st…
Solving Multi-Group Neutron Diffusion Eigenvalue Problem with Decoupling Residual Loss Function
Shupei Yu, Qiaolin He, Shiquan Zhang +3
In the midst of the neural network's success in solving partial differential equations, tackling eigenvalue problems using neural networks remains a challenging task. However, the…
A novel number-theoretic sampling method for neural network solutions of partial differential equations
Yu Yang, Pingan He, Xiaoling Peng +1
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning fram…
Deep FBSDE Neural Networks for Solving Incompressible Navier-Stokes Equation and Cahn-Hilliard Equation
Yangtao Deng, Qiaolin He
Efficient algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the curse of dimensionality.…
Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE
Yu Yang, Qihong Yang, Yangtao Deng +1
In this work, we propose an end-to-end adaptive sampling neural network (MMPDE-Net) based on the moving mesh method, which can adaptively generate new sampling points by solving th…
Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems
Qihong Yang, Yangtao Deng, Yu Yang +2
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar…