A Mesh-less Method Based on Artificial Neural Network for Solving Poisson Equation

摘要

A new mesh-less method based on artificial neural network is presented for solving Poisson equation. Artificial neural network functions are used as trial functions instead of traditional superposition of basis functions. The least square method is adopted to construct the error function according to the electromagnetic problems. Minimization of the error function is implemented by adjusting the neural network parameters using gradient descent method. The new algorithm avoids the storage and solution of massive matrix equations.