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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…
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…
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…