Solving differential equations with neural networks: implementation on a DSP platform

Abstract

Artificial neural networks have been successfully employed for the solution of ordinary and partial differential equations. According to this methodology, the solution to a differential equation is written as a sum of two parts. The first part satisfies the initial/boundary conditions and contains no adjustable parameters. The second part involves a feedforward neural network (MLP) whose weights must be adjusted in order to solve the equation. A significant advantage of the above methodology is the ability of of direct hardware implementation of both the solution and the training procedure. In this work we describe the implementation of the method on a hardware platform with two digital signal processors. We address several implementation and performance issues and provide comparative results against a PC-based implementation of the method.