论文｜Yu Yang, Qihong Yang, Yangtao Deng, Qiaolin He：Moving sampling physics-informed neural networks induced by moving mesh PDE

本文（Moving sampling physics-informed neural networks induced by moving mesh PDE）原载 Neural Networks，由四川大学贺巧琳教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract: In this work, we propose an end-to-end adaptive sampling framework based on deep neural networks and the moving mesh method (MMPDE-Net), 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 sampling points distribute more precisely and controllably. Since MMPDE-Net is independent of the deep learning solver, we combine it with physics-informed neural networks (PINN) to propose moving sampling PINN (MS-PINN) and show the error estimate of our method 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.

 Yu Yang, Qihong Yang, Yangtao Deng, Qiaolin He，Moving sampling physics-informed neural networks induced by moving mesh PDE，Neural Network，2024.（论文下载）