Moving Sampling Physics-informed Neural Networks induced by Moving Mesh PDE
This work addresses the challenge of optimizing sampling points for PINNs, which is incremental as it builds on existing PINN methods to enhance accuracy and control in solving PDEs.
The paper tackles the problem of improving sampling point generation in physics-informed neural networks (PINNs) by proposing an adaptive sampling framework called MMPDE-Net, which uses a moving mesh method to generate new points, and integrates it into MS-PINN, demonstrating performance improvements over standard PINNs in numerical experiments on four examples.
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.