A neural network algorithm for heat conduction interface problems

Abstract:

This paper discusses a single hidden neural network algorithm for the heat conduction interface problems. The proposed algorithm sets the approximate solution to contain a neural network function and to meet the initial/boundary conditions and the Dirichlet interface condition, and trains the neural network by solving the discrete optimization problem derived from the original system so as to finally obtain the approximate solution. A new optimization algorithm based on the stochastic gradient method is also given to solve the corresponding discrete optimization problem. Numerical examples are provided to verify the effectiveness of the neural network algorithm.