Learning high-order geometric flow based on the level set method

Recently, the development of deep learning has accomplished unbelievable success in many fields, especially in scientific computational fields. And almost all computational problems and physical phenomena can be described by partial differential equations. In this work, we proposed two potential high-order geometric flows. Motivation by the physical-information neural networks and the traditional level set method (LSM), we have integrated deep neural networks and LSM to make the proposed method more robust and efficient. Also, to test the sensitivity of the system to different input data, we set up three sets of initial conditions to test the model. Furthermore, numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach.