Special Session 151: Encounter and Merging of Mesh-based Methods and Meshless Methods in the Era of Machine Learning

Some trainer friendly meshless methods
Shuo Zhang
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Peoples Rep of China
Co-Author(s):    
Abstract:
The training process for the neural network problems may suffer from the super parameters and the non-convex formulation. Typical examples include the boundary condition imposition by penalty and the problem of saddle-point essence. This talk discusses how to impose the boundary condition for PINN and how to solve the saddle-point formulation physical model in friendly ways. The main proposal is to formulate the problems as convex energy-minimization problems to be friendly for optimizers. Though neural network problems are used for illustration, the methods essentially work for general meshless methods.