Multilayer perceptrons as function approximators for analytical solutions of the diffusion equation

A novel method using neural networks to analyse diffusion profiles is presented. Multilayer perceptrons are used to approximate the analytical solution of the diffusion equation and find within it any unknown parameter that best fits a given data set. An example based on published data of diffusion of helium is examined to illustrate the main steps of the method. The exercise shows that it is possible to refine the value of diffusion coefficients up to two orders of magnitude in terms of precision. A particular feature of the method is that calibration curves can be taken into account when choosing the best setup of a network, which allows minimization of instrument specific error. A general version of the method giving the opportunity to define a local diffusion coefficient is also discussed, which could be considered for cases where the analytical solution of the diffusion equation cannot be identified a priori or does not exist.