NUMERICAL-SOLUTION OF A CALCULUS OF VARIATIONS PROBLEM USING THE FEEDFORWARD NEURAL-NETWORK ARCHITECTURE

It is demonstrated, through theory and numerical example, how it is po ssible to construct directly and noniteratively a feedforward neural n etwork to solve a calculus of variations problem. The method, using th e piecewise linear and cubic sigmoid transfer functions, is linear in storage and processing time. The L(2) norm of the network approximatio n error decreases quadratically with the piecewise linear transfer fun ction and quartically with the piecewise cubic sigmoid as the number o f hidden layer neurons increases. The construction requires imposing c ertain constraints on the values of the input, bias, and output weight s, and the attribution of certain roles to each of these parameters. A ll results presented used the piecewise linear and cubic sigmoid trans fer functions. However, the noniterative approach should also be appli cable to the use of hyperbolic tangents and radial basis functions. Co pyright (C) 1996 Elsevier Science Limited.