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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 newsampling points by solving the moving mesh PDE. This model focuses on improvingthe quality of sampling points generation. Moreover, we develop an iterativealgorithm based on MMPDE-Net, which makes the sampling points more precise andcontrollable. Since MMPDE-Net is a framework independent of the deep learningsolver, we combine it with physics-informed neural networks (PINN) to proposemoving sampling PINN (MS-PINN) and demonstrate its effectiveness by erroranalysis under some assumptions. Finally, we demonstrate the performanceimprovement of MS-PINN compared to PINN through numerical experiments of fourtypical examples, which numerically verify the effectiveness of our method.

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