Design optimal neural network based on new LM training algorithm for solving 3D - PDEs

Abstract

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

Keywords

• Partial Differenstial Equations
• Neural networks
• BP-training algorithm
• Unconstrained optimization
• LM training algorithm
• Convergence analysis