Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE

• URL: http://arxiv.org/abs/2311.16167v4
• Date: Sun, 9 Jun 2024 08:56:30 GMT
• Title: Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE
• Authors: Yu Yang, Qihong Yang, Yangtao Deng, Qiaolin He,
• Abstract summary: We propose an end-to-end adaptive sampling neural network (MMPDE-Net) based on the moving mesh method. We develop an iterative algorithm based on MMPDE-Net, which makes the sampling points more precise and controllable.
• Score: 4.460242992367118
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 the moving mesh PDE. This model focuses on improving the quality of sampling points generation. Moreover, we develop an iterative algorithm based on MMPDE-Net, which makes the sampling points more precise and controllable. Since MMPDE-Net is a framework independent of the deep learning solver, we combine it with physics-informed neural networks (PINN) to propose moving sampling PINN (MS-PINN) and demonstrate its effectiveness by error analysis under some assumptions. Finally, we demonstrate the performance improvement of MS-PINN compared to PINN through numerical experiments of four typical examples, which numerically verify the effectiveness of our method.

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