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math.NA2026
A Multi-Level Deep Framework for Deep Solvers of Partial Differential Equations
Yu Yang, Qiaolin He
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of…
math.NA2025
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…
math.NA2024
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…